Fresnel equations - Knowledge

16950: 3566: 3034: 7356: 1991: 1569: 3561:{\displaystyle {\begin{aligned}r_{\text{s}}&={\frac {n_{1}\cos \theta _{\text{i}}-n_{2}\cos \theta _{\text{t}}}{n_{1}\cos \theta _{\text{i}}+n_{2}\cos \theta _{\text{t}}}},\\t_{\text{s}}&={\frac {2n_{1}\cos \theta _{\text{i}}}{n_{1}\cos \theta _{\text{i}}+n_{2}\cos \theta _{\text{t}}}},\\r_{\text{p}}&={\frac {n_{2}\cos \theta _{\text{i}}-n_{1}\cos \theta _{\text{t}}}{n_{2}\cos \theta _{\text{i}}+n_{1}\cos \theta _{\text{t}}}},\\t_{\text{p}}&={\frac {2n_{1}\cos \theta _{\text{i}}}{n_{2}\cos \theta _{\text{i}}+n_{1}\cos \theta _{\text{t}}}}.\end{aligned}}} 6989: 1573: 1151: 2820: 2812: 13317: 12954: 7679: 64: 580: 572: 4443:. Fresnel promptly confirmed by experiment that the equations correctly predicted the direction of polarization of the reflected beam when the incident beam was polarized at 45° to the plane of incidence, for light incident from air onto glass or water; in particular, the equations gave the correct polarization at Brewster's angle. The experimental confirmation was reported in a "postscript" to the work in which Fresnel first revealed his theory that light waves, including "unpolarized" waves, were 6644: 7351:{\displaystyle {\begin{aligned}\mathbf {k} _{\text{i}}&=n_{1}k(\mathbf {i} \sin \theta _{\text{i}}+\mathbf {j} \cos \theta _{\text{i}})\\\mathbf {k} _{\text{r}}&=n_{1}k(\mathbf {i} \sin \theta _{\text{i}}-\mathbf {j} \cos \theta _{\text{i}})\\\mathbf {k} _{\text{t}}&=n_{2}k(\mathbf {i} \sin \theta _{\text{t}}+\mathbf {j} \cos \theta _{\text{t}})\\&=k(\mathbf {i} \,n_{1}\sin \theta _{\text{i}}+\mathbf {j} \,n_{2}\cos \theta _{\text{t}})\,,\end{aligned}}} 55: 1986:{\displaystyle R_{\mathrm {p} }=\left|{\frac {n_{1}\cos \theta _{\mathrm {t} }-n_{2}\cos \theta _{\mathrm {i} }}{n_{1}\cos \theta _{\mathrm {t} }+n_{2}\cos \theta _{\mathrm {i} }}}\right|^{2}=\left|{\frac {n_{1}{\sqrt {1-\left({\frac {n_{1}}{n_{2}}}\sin \theta _{\mathrm {i} }\right)^{2}}}-n_{2}\cos \theta _{\mathrm {i} }}{n_{1}{\sqrt {1-\left({\frac {n_{1}}{n_{2}}}\sin \theta _{\mathrm {i} }\right)^{2}}}+n_{2}\cos \theta _{\mathrm {i} }}}\right|^{2}\!.} 1564:{\displaystyle R_{\mathrm {s} }=\left|{\frac {n_{1}\cos \theta _{\mathrm {i} }-n_{2}\cos \theta _{\mathrm {t} }}{n_{1}\cos \theta _{\mathrm {i} }+n_{2}\cos \theta _{\mathrm {t} }}}\right|^{2}=\left|{\frac {n_{1}\cos \theta _{\mathrm {i} }-n_{2}{\sqrt {1-\left({\frac {n_{1}}{n_{2}}}\sin \theta _{\mathrm {i} }\right)^{2}}}}{n_{1}\cos \theta _{\mathrm {i} }+n_{2}{\sqrt {1-\left({\frac {n_{1}}{n_{2}}}\sin \theta _{\mathrm {i} }\right)^{2}}}}}\right|^{2}\!,} 248: 12980: 12617: 7376: 10336: 8535: 9945: 323: 16733: 10574: 8777: 13312:{\displaystyle T_{\text{p}}=\left({\frac {2Y_{1}\cos \theta _{\text{i}}}{Y_{2}\cos \theta _{\text{i}}+Y_{1}\cos \theta _{\text{t}}}}\right)^{2}{\frac {\,Y_{2}\,}{Y_{1}}}\,{\frac {\cos \theta _{\text{t}}}{\cos \theta _{\text{i}}}}={\frac {4Y_{1}Y_{2}\cos \theta _{\text{i}}\cos \theta _{\text{t}}}{\left(Y_{2}\cos \theta _{\text{i}}+Y_{1}\cos \theta _{\text{t}}\right)^{2}}}} 12949:{\displaystyle T_{\text{s}}=\left({\frac {2Y_{1}\cos \theta _{\text{i}}}{Y_{1}\cos \theta _{\text{i}}+Y_{2}\cos \theta _{\text{t}}}}\right)^{2}{\frac {\,Y_{2}\,}{Y_{1}}}\,{\frac {\cos \theta _{\text{t}}}{\cos \theta _{\text{i}}}}={\frac {4Y_{1}Y_{2}\cos \theta _{\text{i}}\cos \theta _{\text{t}}}{\left(Y_{1}\cos \theta _{\text{i}}+Y_{2}\cos \theta _{\text{t}}\right)^{2}}}} 7674:{\displaystyle {\begin{aligned}\mathbf {k} _{\text{i}}\mathbf {\cdot r} &=n_{1}k(x\sin \theta _{\text{i}}+y\cos \theta _{\text{i}})\\\mathbf {k} _{\text{r}}\mathbf {\cdot r} &=n_{1}k(x\sin \theta _{\text{i}}-y\cos \theta _{\text{i}})\\\mathbf {k} _{\text{t}}\mathbf {\cdot r} &=k(n_{1}x\sin \theta _{\text{i}}+n_{2}y\cos \theta _{\text{t}})\,.\end{aligned}}} 12554: 12338: 10109: 8308: 8992: 10786: 1000: 820: 8166: 9751: 7845: 5814: 15189: 15004: 12076: 11892: 10374: 8577: 42: 5636: 11472:

incidence, under the adopted sign convention, the transmission coefficients for the two polarizations are equal, whereas the reflection coefficients have equal magnitudes but opposite signs. While this clash of signs is a disadvantage of the convention, the attendant advantage is that the signs agree

16378:

A. Fresnel, "Mémoire sur la double réfraction que les rayons lumineux éprouvent en traversant les aiguilles de cristal de roche suivant les directions parallèles à l'axe" ("Memoir on the double refraction that light rays undergo in traversing the needles of quartz in the directions parallel to the

14281: 13974: 10976: 9182: 4572:: linearly-polarized light can be resolved into two circularly-polarized components rotating in opposite directions, and if these propagate at different speeds, the phase difference between them — hence the orientation of their linearly-polarized resultant — will vary continuously with distance. 13581:) cancel out, and all the reflection and transmission ratios become independent of the angle of incidence; in other words, the ratios for normal incidence become applicable to all angles of incidence. When extended to spherical reflection or scattering, this results in the Kerker effect for 3023:

is complex) or total internal reflection, the angle of transmission does not generally evaluate to a real number. In that case, however, meaningful results can be obtained using formulations of these relationships in which trigonometric functions and geometric angles are avoided; the

2729:

with an error of less than about 3% for most common optical materials. This is useful because measurements at normal incidence can be difficult to achieve in an experimental setup since the incoming beam and the detector will obstruct each other. However, since the dependence of

10007: direction ("into the page") and may therefore be described by their components in that direction. This is consistent with the adopted sign convention, namely that a positive reflection or transmission coefficient is one that preserves the direction of the transverse field 829: 649: 10331:{\displaystyle {\begin{aligned}H_{\text{i}}&=\,Y_{1}e^{i\mathbf {k} _{\text{i}}\mathbf {\cdot r} }\\H_{\text{r}}&=\,Y_{1}r_{p\,}e^{i\mathbf {k} _{\text{r}}\mathbf {\cdot r} }\\H_{\text{t}}&=\,Y_{2}t_{p\,}e^{i\mathbf {k} _{\text{t}}\mathbf {\cdot r} }.\end{aligned}}} 8530:{\displaystyle {\begin{aligned}H_{\text{i}}&=\,Y_{1}e^{i\mathbf {k} _{\text{i}}\mathbf {\cdot r} }\\H_{\text{r}}&=\,Y_{1}r_{s\,}e^{i\mathbf {k} _{\text{r}}\mathbf {\cdot r} }\\H_{\text{t}}&=\,Y_{2}t_{s\,}e^{i\mathbf {k} _{\text{t}}\mathbf {\cdot r} }.\end{aligned}}} 12364: 12148: 10029:

field with the red arrows reveals an alternative definition of the sign convention: that a positive reflection or transmission coefficient is one for which the field vector in the plane of incidence points towards the same medium before and after reflection or transmission.

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Thus Fresnel's interpretation of the complex values of his reflection coefficients marked the confluence of several streams of his research and, arguably, the essential completion of his reconstruction of physical optics on the transverse-wave hypothesis (see

9940:{\displaystyle {\begin{aligned}E_{\text{i}}&=e^{i\mathbf {k} _{\text{i}}\mathbf {\cdot r} }\\E_{\text{r}}&=r_{p\,}e^{i\mathbf {k} _{\text{r}}\mathbf {\cdot r} }\\E_{\text{t}}&=t_{p\,}e^{i\mathbf {k} _{\text{t}}\mathbf {\cdot r} }.\end{aligned}}} 7706: 5549: 15682:

and any beam reflected at that angle will be p-polarized instead of s-polarized. Similarly, Fresnel's sine law will apply to the p polarization instead of the s polarization, and his tangent law to the s polarization instead of the p polarization.

4427:[T]he great difficulty of all, which is to assign a sufficient reason for the reflection or nonreflection of a polarised ray, will probably long remain, to mortify the vanity of an ambitious philosophy, completely unresolved by any theory. 15027: 16275:

A. Fresnel, "Mémoire sur la loi des modifications que la réflexion imprime à la lumière polarisée" ("Memoir on the law of the modifications that reflection impresses on polarized light"), read 7 January 1823; reprinted in Fresnel, 1866,

14846: 11918: 11734: 10569:{\displaystyle \left.{\begin{aligned}E_{\text{i}}\cos \theta _{\text{i}}-E_{\text{r}}\cos \theta _{\text{i}}&=E_{\text{t}}\cos \theta _{\text{t}}\\H_{\text{i}}+H_{\text{r}}&=H_{\text{t}}\end{aligned}}~~\right\}~~~{\text{at}}~~y=0\,.} 8772:{\displaystyle \left.{\begin{aligned}E_{\text{i}}+E_{\text{r}}&=E_{\text{t}}\\H_{\text{i}}\cos \theta _{\text{i}}-H_{\text{r}}\cos \theta _{\text{i}}&=H_{\text{t}}\cos \theta _{\text{t}}\end{aligned}}~~\right\}~~~{\text{at}}~~y=0\,.} 2681:, or to derive one of them when the other is known. This relationship is only valid for the simple case of a single plane interface between two homogeneous materials, not for films on substrates, where a more complex analysis is required. 2271: 13790: 3813: 4342:

with one another, resulting in net transmission and reflection amplitudes that depend on the light's wavelength. The interference, however, is seen only when the surfaces are at distances comparable to or smaller than the light's

5936: 14138: 13831: 10833: 9039: 539: 13520:), we see that two dissimilar media will have the same refractive index, but different admittances, if the ratio of their permeabilities is the inverse of the ratio of their permittivities. In that unusual situation we have 2172:

Although these relationships describe the basic physics, in many practical applications one is concerned with "natural light" that can be described as unpolarized. That means that there is an equal amount of power in the

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Note that all such intensities are measured in terms of a wave's irradiance in the direction normal to the interface; this is also what is measured in typical experiments. That number could be obtained from irradiances

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on the angle of incidence for angles below 10° is very small, a measurement at about 5° will usually be a good approximation for normal incidence, while allowing for a separation of the incoming and reflected beam.

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calculating the angle of incidence that would introduce a total phase difference of 90° between the s and p components, for various numbers of total internal reflections at that angle (generally there were two

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Although it is not encountered in practice, the equations can also apply to the case of two media with a common permittivity but different refractive indices due to different permeabilities. From equations

12549:{\displaystyle T_{\text{p}}=1-R_{\text{p}}=\,{\frac {4\,{\text{Re}}\{Y_{1}Y_{2}\cos \theta _{\text{i}}\cos \theta _{\text{t}}\}}{\left|Y_{2}\cos \theta _{\text{i}}+Y_{1}\cos \theta _{\text{t}}\right|^{2}}}} 12333:{\displaystyle T_{\text{s}}=1-R_{\text{s}}=\,{\frac {4\,{\text{Re}}\{Y_{1}Y_{2}\cos \theta _{\text{i}}\cos \theta _{\text{t}}\}}{\left|Y_{1}\cos \theta _{\text{i}}+Y_{2}\cos \theta _{\text{t}}\right|^{2}}}} 14820: 11355: 9561: 456: 2983: 6238: 14622: 8987:{\displaystyle {\begin{aligned}1+r_{\text{s}}&=\,t_{\text{s}}\\Y_{1}\cos \theta _{\text{i}}-Y_{1}r_{\text{s}}\cos \theta _{\text{i}}&=\,Y_{2}t_{\text{s}}\cos \theta _{\text{t}}\,,\end{aligned}}} 2780:

ratios of those EM fields and may take several different forms, depending on the formalism used. The complex amplitude coefficients for reflection and transmission are usually represented by lower case

10781:{\displaystyle {\begin{aligned}\cos \theta _{\text{i}}-r_{\text{p}}\cos \theta _{\text{i}}&=\,t_{\text{p}}\cos \theta _{\text{t}}\\Y_{1}+Y_{1}r_{\text{p}}&=\,Y_{2}t_{\text{p}}\,.\end{aligned}}} 14304: 11002: 9208: 5520: 13997: 6171: 15517: 10623: 10383: 10114: 9756: 8826: 8586: 8313: 8028: 7381: 5869: 5726: 5554: 4646: 2121: 2071: 6337: 995:{\displaystyle R_{\mathrm {p} }=\left|{\frac {Z_{2}\cos \theta _{\mathrm {t} }-Z_{1}\cos \theta _{\mathrm {i} }}{Z_{2}\cos \theta _{\mathrm {t} }+Z_{1}\cos \theta _{\mathrm {i} }}}\right|^{2},} 815:{\displaystyle R_{\mathrm {s} }=\left|{\frac {Z_{2}\cos \theta _{\mathrm {i} }-Z_{1}\cos \theta _{\mathrm {t} }}{Z_{2}\cos \theta _{\mathrm {i} }+Z_{1}\cos \theta _{\mathrm {t} }}}\right|^{2},} 8161:{\displaystyle {\begin{aligned}E_{\text{r}}&=r_{s\,}e^{i\mathbf {k} _{\text{r}}\mathbf {\cdot r} }\\E_{\text{t}}&=t_{s\,}e^{i\mathbf {k} _{\text{t}}\mathbf {\cdot r} }.\end{aligned}}} 6002: 1126: 1052:), which is typically a good approximation at optical frequencies (and for transparent media at other frequencies). Then the wave impedances are determined solely by the refractive indices 6085: 2659: 300:

to the plane of incidence. The names "s" and "p" for the polarization components refer to German "senkrecht" (perpendicular or normal) and "parallel" (parallel to the plane of incidence).

13647: 13466: 13405: 7840:{\displaystyle y=0\,,~~~\mathbf {k} _{\text{i}}\mathbf {\cdot r} =\mathbf {k} _{\text{r}}\mathbf {\cdot r} =\mathbf {k} _{\text{t}}\mathbf {\cdot r} =n_{1}kx\sin \theta _{\text{i}}\,.} 6392: 2188: 3014: 2937: 15895:. Although the imaginary unit does not appear explicitly in the results given here, the time-dependent factor affects the interpretation of any results that turn out to be complex. 13670: 3715: 16917:– Web interface for calculating optical properties of thin films and multilayer materials (reflection & transmission coefficients, ellipsometric parameters Psi & Delta). 5809:{\displaystyle {\begin{aligned}\omega \mu \mathbf {H} &=\mathbf {k} \times \mathbf {E} \\\omega \epsilon \mathbf {E} &=-\mathbf {k} \times \mathbf {H} \,.\end{aligned}}} 2702:

at 45° can be used to estimate the reflectivity at normal incidence. The "average of averages" obtained by calculating first the arithmetic as well as the geometric average of

15184:{\displaystyle R_{\text{p}}=\left|{\frac {n_{2}\cos \theta _{\text{i}}-n_{1}\cos \theta _{\text{t}}}{n_{2}\cos \theta _{\text{i}}+n_{1}\cos \theta _{\text{t}}}}\right|^{2}\,.} 5435: 30:

This article is about the Fresnel equations describing reflection and refraction of light at uniform planar interfaces. For the diffraction of light through an aperture, see

5334: 14999:{\displaystyle R_{\text{s}}=\left|{\frac {n_{1}\cos \theta _{\text{i}}-n_{2}\cos \theta _{\text{t}}}{n_{1}\cos \theta _{\text{i}}+n_{2}\cos \theta _{\text{t}}}}\right|^{2}} 12071:{\displaystyle R_{\text{p}}=\left|{\frac {Y_{2}\cos \theta _{\text{i}}-Y_{1}\cos \theta _{\text{t}}}{Y_{2}\cos \theta _{\text{i}}+Y_{1}\cos \theta _{\text{t}}}}\right|^{2}} 11887:{\displaystyle R_{\text{s}}=\left|{\frac {Y_{1}\cos \theta _{\text{i}}-Y_{2}\cos \theta _{\text{t}}}{Y_{1}\cos \theta _{\text{i}}+Y_{2}\cos \theta _{\text{t}}}}\right|^{2}} 13335:

for the p polarization. The last two equations apply only to lossless dielectrics, and only at incidence angles smaller than the critical angle (beyond which, of course,

5864: 4546:

Four weeks before he presented his completed theory of total internal reflection and the rhomb, Fresnel submitted a memoir in which he introduced the needed terms

11657:. To compute the irradiance in the direction normal to the interface, as we shall require in the definition of the power transmission coefficient, we could use only the 3688: 465: 16527:

More general Brewster angles, for which the angles of incidence and refraction are not necessarily complementary, are discussed in C.L. Giles and W.J. Wild,

2591:

Reflection at 45° incidence is very commonly used for making 90° turns. For the case of light traversing from a less dense medium into a denser one at 45° incidence (

563:) is what can be directly measured at optical frequencies. The power of a wave is generally proportional to the square of the electric (or magnetic) field amplitude. 15692:, above). One could predict reflection coefficients that agreed with observation by supposing (like Fresnel) that different refractive indices were due to different 13498: 5631:{\displaystyle {\begin{aligned}\omega \mathbf {B} &=\mathbf {k} \times \mathbf {E} \\\omega \mathbf {D} &=-\mathbf {k} \times \mathbf {H} \,.\end{aligned}}} 5459:, which is understood to multiply every complex field quantity. The electric field for a uniform plane sine wave will then be represented by the location-dependent 4503:

subjecting light to that number of total internal reflections at that angle of incidence, with an initial linear polarization at 45° to the plane of incidence, and

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and positive), one can obtain these results directly using the squared magnitudes of the amplitude transmission coefficients that we found earlier in equations (

3632:

Because the reflected and incident waves propagate in the same medium and make the same angle with the normal to the surface, the power reflection coefficient

4473:

In the same memoir of January 1823, Fresnel found that for angles of incidence greater than the critical angle, his formulas for the reflection coefficients (

310:) there is no distinction between them so all polarization states are governed by a single set of Fresnel coefficients (and another special case is mentioned 6248: 3894:) but has nonzero values very close to the interface. The phase shift of the reflected wave on total internal reflection can similarly be obtained from the 3696:

is less straightforward, since the light travels in different directions in the two media. What's more, the wave impedances in the two media differ; power (

14276:{\displaystyle r_{\text{p}}={\frac {n_{2}\cos \theta _{\text{i}}-n_{1}\cos \theta _{\text{t}}}{n_{2}\cos \theta _{\text{i}}+n_{1}\cos \theta _{\text{t}}}}} 13969:{\displaystyle r_{\text{s}}={\frac {n_{1}\cos \theta _{\text{i}}-n_{2}\cos \theta _{\text{t}}}{n_{1}\cos \theta _{\text{i}}+n_{2}\cos \theta _{\text{t}}}}} 10971:{\displaystyle r_{\text{p}}={\frac {Y_{2}\cos \theta _{\text{i}}-Y_{1}\cos \theta _{\text{t}}}{Y_{2}\cos \theta _{\text{i}}+Y_{1}\cos \theta _{\text{t}}}}} 9177:{\displaystyle r_{\text{s}}={\frac {Y_{1}\cos \theta _{\text{i}}-Y_{2}\cos \theta _{\text{t}}}{Y_{1}\cos \theta _{\text{i}}+Y_{2}\cos \theta _{\text{t}}}}} 3025: 555:. The ratio of waves' electric field (or magnetic field) amplitudes are obtained, but in practice one is more often interested in formulae which determine 16713: 3629:. One can write very similar equations applying to the ratio of the waves' magnetic fields, but comparison of the electric fields is more conventional. 2151:

of the Poynting vector with the unit vector normal to the interface). This complication can be ignored in the case of the reflection coefficient, since

5240:, where the last factor contains the time-dependence. That factor also implies that differentiation w.r.t. time corresponds to multiplication by 218:

fields can also be related using similar coefficients.) These ratios are generally complex, describing not only the relative amplitudes but also the

16442:

Compare M.V. Berry and M.R. Jeffrey, "Conical diffraction: Hamilton's diabolical point at the heart of crystal optics", in E. Wolf (ed.),

414: 9683:

fields are parallel to the red arrows and may therefore be described by their components in the directions of those arrows. Let those components be

7939: 8554: 6399: 6557: 3951: 2861:

is the ratio of the transmitted wave's complex electric field amplitude to that of the incident wave, for either polarization. The coefficients

4491:) gave complex values with unit magnitudes. Noting that the magnitude, as usual, represented the ratio of peak amplitudes, he guessed that the 15848:(2.81)]. The electrical engineers' form and the formulas derived therefrom may be converted to the physicists' convention by substituting 15720:

to that plane. Thus the condition of equal permittivities and unequal permeabilities, although not realistic, is of some historical interest.

8184:

Under the sign convention used in this article, a positive reflection or transmission coefficient is one that preserves the direction of the

4873:) to the speed of light in the medium. In the analysis of partial reflection and transmission, one is also interested in the electromagnetic 6481: 4374:. A quantitative analysis of these effects is based on the Fresnel equations, but with additional calculations to account for interference. 4981: 4411:

to describe this behavior. In 1815, the dependence of the polarizing angle on the refractive index was determined experimentally by

13792:

that is, the admittances are simply proportional to the corresponding refractive indices. When we make these substitutions in equations (

2562:, occurs at incidence angles for which Snell's law predicts that the sine of the angle of refraction would exceed unity (whereas in fact 2169:, so that the ratio of reflected to incident irradiance in the wave's direction is the same as in the direction normal to the interface. 2076: 2026: 15785: 4450:

Details of Fresnel's derivation, including the modern forms of the sine law and tangent law, were given later, in a memoir read to the

14645: 14451: 11177: 9383: 5855:, so that the same equations apply to the magnitudes of the respective vectors. Taking the magnitude equations and substituting from ( 4831:

must be taken into account. But, for optically transparent media, and for all other materials at optical frequencies (except possible

1073: 264: 14747: 11282: 9488: 16741: 16485:

Giles, C.L.; Wild, W.J. (1982). "Fresnel Reflection and Transmission at a Planar Boundary from Media of Equal Refractive Indices".

11497:(power per unit area) of that wave on a surface perpendicular to that direction. For a plane sinusoidal wave the Poynting vector is 2944: 2619: 14420:{\displaystyle t_{\text{p}}={\frac {2n_{1}\cos \theta _{\text{i}}}{n_{2}\cos \theta _{\text{i}}+n_{1}\cos \theta _{\text{t}}}}\,.} 12609:. Applying these corrections to each wave, we obtain two ratios multiplying the square of the amplitude transmission coefficient: 11118:{\displaystyle t_{\text{p}}={\frac {2Y_{1}\cos \theta _{\text{i}}}{Y_{2}\cos \theta _{\text{i}}+Y_{1}\cos \theta _{\text{t}}}}\,.} 9324:{\displaystyle t_{\text{s}}={\frac {2Y_{1}\cos \theta _{\text{i}}}{Y_{1}\cos \theta _{\text{i}}+Y_{2}\cos \theta _{\text{t}}}}\,.} 6185: 2483:

goes to zero and a p-polarised incident wave is purely refracted, thus all reflected light is s-polarised. This angle is known as

16970: 14553: 14110:{\displaystyle t_{\text{s}}={\frac {2n_{1}\cos \theta _{\text{i}}}{n_{1}\cos \theta _{\text{i}}+n_{2}\cos \theta _{\text{t}}}}\,} 13608: 4171:{\displaystyle r_{\text{s}}=-{\frac {\sin(\theta _{\text{i}}-\theta _{\text{t}})}{\sin(\theta _{\text{i}}+\theta _{\text{t}})}}.} 13409: 13348: 4296:{\displaystyle r_{\text{p}}={\frac {\tan(\theta _{\text{i}}-\theta _{\text{t}})}{\tan(\theta _{\text{i}}+\theta _{\text{t}})}}.} 233:, which is sufficient to solve any problem since any incident light field can be decomposed into plane waves and polarizations. 15840:

for the imaginary unit, but also change the sign of the exponent, with the result that the whole expression is replaced by its

5472: 6123: 16858: 16835: 16816: 16797: 16609: 15951: 15455: 543:

The behavior of light striking the interface is explained by considering the electric and magnetic fields that constitute an

4704:{\displaystyle {\begin{aligned}\mathbf {D} &=\epsilon \mathbf {E} \\\mathbf {B} &=\mu \mathbf {H} \,,\end{aligned}}} 4924:. The last-mentioned relation, however, will make it convenient to derive the reflection coefficients in terms of the wave 2837:

is defined as the ratio of the reflected wave's complex electric field amplitude to that of the incident wave, whereas for

2442:), the power reflectance at normal incidence can be seen to be about 4%, or 8% accounting for both sides of a glass pane. 263:

can be resolved into a combination of two orthogonal linear polarizations, this is sufficient for any problem. Likewise,

6305: 4399:

discovered that when a ray of light was reflected off a non-metallic surface at the appropriate angle, it behaved like

4313:. Although at normal incidence these expressions reduce to 0/0, one can see that they yield the correct results in the 161:

could be understood quantitatively, as Fresnel's equations correctly predicted the differing behaviour of waves of the

73: 17: 16288:

773 (sine law), 757 (tangent law), 760–61 and 792–6 (angles of total internal reflection for given phase differences).

16225:

A. Fresnel, "Note sur le calcul des teintes que la polarisation développe dans les lames cristallisées" et seq.,

11552:

to the wave in question, and the asterisk denotes complex conjugation. Inside a lossless dielectric (the usual case),

251:

The plane of incidence is defined by the incoming radiation's propagation vector and the normal vector of the surface.

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A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century

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normal to the interface, for both the incident and transmitted waves, so that full power transmission corresponds to

13593:

Since the Fresnel equations were developed for optics, they are usually given for non-magnetic materials. Dividing (

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for the p polarization. Note that when comparing the powers of two such waves in the same medium and with the same

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When light makes multiple reflections between two or more parallel surfaces, the multiple beams of light generally

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impedance or admittance of the medium. This case is the one for which the Fresnel coefficients are to be derived.

4731: 4378: 4339: 3647: 12105:, the impedance and geometric factors mentioned above are identical and cancel out. But in computing the power 16241:

609–48; translated as "On the calculation of the tints that polarization develops in crystalline plates, &

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polarized, an artifact of the adopted sign convention (see graph for an air-glass interface at 0° incidence).

260: 214:

wave's electric field to the incident wave's electric field, for each of two components of polarization. (The

16990: 8813:), the exponential factors cancel out, so that the interface conditions reduce to the simultaneous equations 5539: 6359: 4540: 2990: 2913: 583:

Power coefficients: glass to air (Total internal reflection starts from 42° making reflection coefficient 1)

16874:, G.L. Trigg, VHC publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1, ISBN (VHC Inc.) 0-89573-752-3 5543: 16995: 16980: 5212: 4492: 3895: 2907: 16237:

102–11 (May 1821), 167–96 (June 1821), 312–15 ("Postscript", July 1821); reprinted in Fresnel, 1866, pp.

5129:

of the expression is the physical field. The value of the expression is unchanged if the position

2793:(whereas the power coefficients are capitalized). As before, we are assuming the magnetic permeability, 16940: 16926: 15765: 15744: 4598:

In order to compute meaningful Fresnel coefficients, we must assume that the medium is (approximately)

4451: 2280: 1043: 45:

Partial transmission and reflection of a pulse travelling from a low to a high refractive index medium.

16935:

of the transmission and reflection probabilities from a multilayer with complex indices of refraction.

16929:– Mathematica interactive webpage that shows the relations between index of refraction and reflection. 3883:

nevertheless describes the electric field (including its phase) just beyond the interface. This is an

16751: 5399: 4961: 3872: 2559: 2516: 107: 16921:

Simple web interface for calculating single-interface reflection and refraction angles and strengths

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The equations assume the interface between the media is flat and that the media are homogeneous and

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The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century

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fields may therefore be described by their components in the directions of those arrows, denoted by

4495:

represented the phase shift, and verified the hypothesis experimentally. The verification involved

4420: 16155: 9719:(redefining the symbols for the new context). Let the reflection and transmission coefficients be 2761:

for instance) are derived from the Fresnel equations which solve the physical problem in terms of

267:(or "randomly polarized") light has an equal amount of power in each of two linear polarizations. 15739: 6474: 4560: 2317:, and there is no distinction between s and p polarization. Thus, the reflectance simplifies to 1138: 219: 16903: 16897: 2266:{\displaystyle R_{\mathrm {eff} }={\frac {1}{2}}\left(R_{\mathrm {s} }+R_{\mathrm {p} }\right).} 2023:: power per unit area) simply as the portion of the incident power that isn't reflected: 15811: 15592:) are interchanged (due to the additional step of multiplying the numerator and denominator by 4367: 2773: 2016: 2009: 548: 16680: 6986:

in the second medium. From the magnitudes and the geometry, we find that the wave vectors are

4396: 3924:

waves, which is the well-known principle by which total internal reflection is used to effect

635:

each side of an interface and do not account for attenuation of a wave in an absorbing medium

15701: 13785:{\displaystyle Y_{1}={\frac {n_{1}}{\,c\mu _{0}}}~~;~~~Y_{2}={\frac {n_{2}}{\,c\mu _{0}}}\,;} 4603: 4578: 4554: 4539:, beginning in 1836, to analyze reflection from metals by using the Fresnel equations with a 4536: 4507: 4440: 4432: 4390: 3808:{\displaystyle T={\frac {n_{2}\cos \theta _{\text{t}}}{n_{1}\cos \theta _{\text{i}}}}|t|^{2}} 2762: 303:

Although the reflection and transmission are dependent on polarization, at normal incidence (

157:, when no one realized that the waves were electric and magnetic fields. For the first time, 118: 15686:

This switch of polarizations has an analog in the old mechanical theory of light waves (see

4435:

derived results equivalent to his sine and tangent laws (above), by modeling light waves as

4347:, which for ordinary white light is few micrometers; it can be much larger for light from a 16571: 16494: 16156:"On the laws which regulate the polarisation of light by reflexion from transparent bodies" 15245: 13471: 6579: 6200: 6146: 2521:

When light travelling in a denser medium strikes the surface of a less dense medium (i.e.,

544: 256: 199: 158: 81: 12591:). But, for given amplitude (as noted above), the component of the Poynting vector in the 4518:— a device that he had been using in experiments, in one form or another, since 1817 (see 8: 16920: 15760: 15734: 15709: 13650: 5360: 4758: 4548: 4314: 2484: 2451: 31: 16528: 16498: 10610:), the exponential factors again cancel out, so that the interface conditions reduce to 4454:

in January 1823. That derivation combined conservation of energy with continuity of the

4381:, or the recursive Rouard method can be used to solve multiple-surface problems. 2279:, rather than rigorously computing the effective reflection coefficient for each angle, 288:

the plane of incidence. The p polarization refers to polarization of the electric field

16847: 16786: 16510: 15780: 15775: 277: 242: 16932: 16685:

Report of the Fourth Meeting of the British Association for the Advancement of Science

16459: 3028:

launched into the second medium cannot be described using a single propagation angle.

16881: 16854: 16831: 16812: 16793: 16669: 16654: 16639: 16605: 16583: 16514: 15947: 15889:. This article, however, uses the physics convention, whose time-dependent factor is 15878:, so that a phase advance corresponds to multiplication by a complex constant with a 15844:, leaving the real part unchanged [Cf. (e.g.) Collin, 1966, p. 41, eq. 15841: 15770: 8188:

field, meaning (in this context) the field normal to the plane of incidence. For the

5116: 5106: 4520: 2765: 2276: 823: 643: 408: 5931:{\displaystyle {\begin{aligned}\mu cH&=nE\\\epsilon cE&=nH\,,\end{aligned}}} 16502: 16455: 16256: 15939: 15705: 4861: 4565: 4532: 4344: 3884: 2297: 178: 124: 76:

incidence, media interfaces appear mirror-like especially due to reflection of the

16699: 16185:

Supplement to the Fourth, Fifth, and Sixth Editions of the Encyclopædia Britannica

15990: 2819: 2811: 534:{\displaystyle n_{1}\sin \theta _{\mathrm {i} }=n_{2}\sin \theta _{\mathrm {t} }.} 210:

wave's electric field to the incident wave's electric field, and the ratio of the

16709: 16624: 15986: 15755: 11487: 4590:

Here we systematically derive the above relations from electromagnetic premises.

4467: 3916:(whose magnitudes are unity in this case). These phase shifts are different for 2131: 588: 154: 111: 15882:

argument, and differentiation w.r.t. time corresponds to multiplication by

13545:(that is, the transmitted ray is undeviated), so that the cosines in equations ( 2720:, and then averaging these two averages again arithmetically, gives a value for 16975: 16954: 16908: 16871: 15729: 15637:

in terms of refractive indices will be interchanged, so that Brewster's angle (

15406: 13582: 6902: 5338: 5078: 4965: 4874: 4412: 4371: 3705: 2855:

of the ratio of their electric field amplitudes). The transmission coefficient

2827:

In the following equations and graphs, we adopt the following conventions. For

2777: 2005: 1021: 459: 377: 12575:

In the case of an interface between two lossless media (for which ϵ and μ are

1148:. Making this substitution, we obtain equations using the refractive indices: 16964: 15749: 15405:

and only the s-polarized component is reflected. This is what happens at the

12114: 6915:), the magnitude of the wave vector is proportional to the refractive index. 5154: 4819: 4569: 4404: 3925: 2769: 2752: 613: 579: 571: 566: 272: 16807:

Griffiths, David J. (2017). "Chapter 9.3: Electromagnetic Waves in Matter".

7992:{\displaystyle E_{\text{i}}=e^{i\mathbf {k} _{\text{i}}\mathbf {\cdot r} },} 6463:{\textstyle Z_{0}={\sqrt {\mu _{0}/\epsilon _{0}}}\,\approx 377\,\Omega \,,} 2413:{\displaystyle R_{0}=\left|{\frac {n_{1}-n_{2}}{n_{1}+n_{2}}}\right|^{2}\,.} 2185:

reflectivity of the material is just the average of the two reflectivities:

16260: 11722: 4832: 4725: 35: 6626:{\displaystyle Z=Z_{0}{\big /}\!{\sqrt {\epsilon _{\text{rel}}}}=Z_{0}/n.} 4808:

In optics it is common to assume that the medium is non-magnetic, so that

4018:{\displaystyle n_{2}=n_{1}\sin \theta _{\text{i}}/\sin \theta _{\text{t}}} 1995:

The second form of each equation is derived from the first by eliminating

611:, and the fraction that is refracted into the second medium is called the 63: 7359: 5088: 4458:

vibration at the interface, but failed to allow for any condition on the

4359: 4355: 2663:

This can be used to either verify the consistency of the measurements of

2148: 593: 376:. The angles that the incident, reflected and refracted rays make to the 16911:– Free software computes the optical properties of multilayer materials. 16696:

History of the Inductive Sciences: From the Earliest to the Present Time

15979: 6643: 41: 15869:

In the electrical engineering convention, the time-dependent factor is

11611: 11564:

are in phase, and at right angles to each other and to the wave vector

11493: 6824: 6538:{\textstyle Z/Z_{0}={\sqrt {\mu _{\text{rel}}/\epsilon _{\text{rel}}}}} 5096: 4941: 3697: 2758: 2020: 560: 331: 230: 203: 6289:{\displaystyle n={\sqrt {\mu _{\text{rel}}\epsilon _{\text{rel}}}}\,.} 407:, respectively. The relationship between these angles is given by the 54: 16475:

This agrees with Born & Wolf, 1970, p. 38, Fig. 1.10.

7894: direction. Let the reflection and transmission coefficients be 4944: 4869:

of the medium, which is the ratio of the speed of light in a vacuum (

4599: 4439:

with vibrations perpendicular to what had previously been called the

3692:

On the other hand, calculation of the power transmission coefficient

2906:

The equations consider a plane wave incident on a plane interface at

270:

The s polarization refers to polarization of a wave's electric field

247: 115: 16506: 16251: 5039:{\displaystyle \mathbf {E_{k}} e^{i(\mathbf {k\cdot r} -\omega t)},} 2881:

polarizations, and even at normal incidence (where the designations

2757:

The above equations relating powers (which could be measured with a

2275:

For low-precision applications involving unpolarized light, such as

255:

There are two sets of Fresnel coefficients for two different linear

206:

of the light may occur. The Fresnel equations give the ratio of the

110:

in general) when incident on an interface between different optical

16828:

Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers

16602:

A History of Optics: From Greek Antiquity to the Nineteenth Century

4607: 4514:

Thus he finally had a quantitative theory for what we now call the

3849:

is the reciprocal of the ratio of the media's wave impedances. The

226: 15943: 9969:

fields are in the directions of the red arrows, then, in order for

5828:

are real (as in a lossless dielectric), these equations show that

2808:

as is essentially true of all dielectrics at optical frequencies.

16556:

Whittaker, 1910, pp. 133, 148–9; Darrigol, 2012, pp. 212, 229–31.

11480: 80:

polarization, despite being poor reflectors at normal incidence.

16914: 16849:

The Light Fantastic – Introduction to Classic and Quantum Optics

16379:

axis"), read 9 December 1822; printed in Fresnel, 1866, pp.

14719:{\displaystyle r_{\text{p0}}={\frac {n_{2}-n_{1}}{n_{2}+n_{1}}}} 14525:{\displaystyle r_{\text{s0}}={\frac {n_{1}-n_{2}}{n_{1}+n_{2}}}} 11251:{\displaystyle r_{\text{p0}}={\frac {Y_{2}-Y_{1}}{Y_{2}+Y_{1}}}} 9457:{\displaystyle r_{\text{s0}}={\frac {Y_{1}-Y_{2}}{Y_{1}+Y_{2}}}} 8015:

and the reflected and transmitted fields, in the same form, are

3017:. In the case of an interface into an absorbing material (where 16246: 12112:

The simplest way to obtain the power transmission coefficient (

11491:

for a wave is a vector whose component in any direction is the

9375:, indicated by an additional subscript 0, these results become 5461: 4436: 4419:

for that dependence was such a deep mystery that in late 1817,

284:

direction in the derivation below); then the magnetic field is

16687:(held at Edinburgh in 1834), London: J. Murray, 1835, pp. 15934:

Driggers, Ronald G.; Hoffman, Craig; Driggers, Ronald (2011).

14815:{\displaystyle t_{\text{p0}}={\frac {2n_{1}}{n_{2}+n_{1}}}\,.} 11350:{\displaystyle t_{\text{p0}}={\frac {2Y_{1}}{Y_{2}+Y_{1}}}\,.} 9556:{\displaystyle t_{\text{s0}}={\frac {2Y_{1}}{Y_{1}+Y_{2}}}\,.} 6866:. Let the angle of refraction, measured in the same sense, be 2895:

is reversed depending on whether the wave is considered to be

451:{\displaystyle \theta _{\mathrm {i} }=\theta _{\mathrm {r} },} 340:

strikes the interface between two media of refractive indices

88:

polarization, greatly reducing glare from horizontal surfaces.

16681:"Report on the progress and present state of physical optics" 11169:

indicated by an additional subscript 0, these results become

5208:

is equivalent to multiplication by a complex constant with a

5198:), with the result that the (complex) field is multiplied by 4348: 2978:{\displaystyle \theta _{\mathrm {r} }=\theta _{\mathrm {i} }} 103: 15580:, with the result that the subscripts 1 and 2 in equations ( 7888:

axis and may therefore be described by its component in the

6839:

directions, respectively. Let the plane of incidence be the

6233:{\displaystyle c=1{\big /}\!{\sqrt {\mu _{0}\epsilon _{0}}}} 6020:

Dividing (or cross-multiplying) the same two equations gives

4025:(Snell's law) and multiply the numerator and denominator by 2799:

of both media to be equal to the permeability of free space

2583:

surrounded by air, the critical angle is approximately 42°.

15752:, Fresnel's apparatus to produce circularly polarised light 14617:{\displaystyle t_{\text{s0}}={\frac {2n_{1}}{n_{1}+n_{2}}}} 10379: 8582: 6845:

plane (the plane of the page), with the angle of incidence

4822:

materials at radio/microwave frequencies, larger values of

4531:

The success of the complex reflection coefficient inspired

322: 296:

plane in the derivation below); then the magnetic field is

142: 133: 16103:

Jenkins & White, 1976, p. 524, eqs. (25a).

15712:) that different refractive indices were due to different 2753:

Complex amplitude reflection and transmission coefficients

2598:), it follows algebraically from the above equations that 567:

Power (intensity) reflection and transmission coefficients

5515:{\displaystyle \mathbf {E_{k}} e^{i\mathbf {k\cdot r} }.} 3700:) is given by the square of the electric field amplitude 2019:, one can find the transmitted power (or more correctly, 15225:

For equal permeabilities (e.g., non-magnetic media), if

9995:

to form a right-handed orthogonal triad, the respective

7919:

field is taken to have unit amplitude, the phasor form (

7358:

where the last step uses Snell's law. The corresponding

6909:

does not change on reflection or refraction. Hence, by (

6166:{\displaystyle c/n=1{\big /}\!{\sqrt {\mu \epsilon \,}}} 4948:

waves, the wave impedance or admittance is known as the

4192:, the result is easily shown to be equivalent to 16623:, Paris: Imprimerie Impériale (3 vols., 1866–70), 16619:

H. de Senarmont, E. Verdet, and L. Fresnel),

15933: 15512:{\displaystyle \theta _{\text{i}}=\arctan(n_{2}/n_{1})} 13823:

cancels out. For the amplitude coefficients we obtain:

9677:

polarization, the incident, reflected, and transmitted

6703:. The red arrows are perpendicular to the wave vectors. 177:

When light strikes the interface between a medium with

16533:

International Journal of Infrared and Millimeter Waves

6484: 6402: 6362: 4354:

An example of interference between reflections is the

3857:

factors adjust the waves' powers so they are reckoned

3708:

of the medium (or by the square of the magnetic field

16938: 16094:

Born & Wolf, 1970, p. 40, eqs. (21a).

15458: 15030: 14849: 14750: 14648: 14556: 14454: 14307: 14141: 14000: 13834: 13673: 13611: 13474: 13412: 13351: 12983: 12620: 12367: 12151: 11921: 11737: 11285: 11180: 11005: 10836: 10621: 10377: 10112: 9754: 9491: 9386: 9211: 9042: 8824: 8580: 8311: 8216:

fields are in the directions of the red arrows, since

8026: 7942: 7709: 7379: 6992: 6685:), for incidence from a medium with refractive index 6560: 6308: 6251: 6188: 6126: 6051: 5969: 5867: 5724: 5552: 5475: 5402: 5363: 5309: 4984: 4644: 4198: 4070: 3954: 3718: 3650: 3037: 2993: 2947: 2916: 2622: 2323: 2191: 2147:

to the normal direction (or equivalently, taking the

2079: 2029: 1576: 1154: 1076: 832: 652: 468: 417: 139: 127: 16698:, 3rd Ed., London: J.W. Parker & Son, 16284:

753–62 (extract, published 1823). See especially pp.

8210:-direction ("out of the page"), then the respective 4362:

or in thin oil films on water. Applications include

2537:), beyond a particular incidence angle known as the 2474:, there is a particular angle of incidence at which 145: 130: 12118:, the ratio of transmitted power to incident power 12109:(below), these factors must be taken into account. 10354:At the interface, the tangential components of the 8198:field. If the incident, reflected, and transmitted 6811:axis is normal to the interface (see diagram). Let 6647:

Incident, reflected, and transmitted wave vectors (

4735:of the medium. For a vacuum, these have the values 2116:{\displaystyle T_{\mathrm {p} }=1-R_{\mathrm {p} }} 2066:{\displaystyle T_{\mathrm {s} }=1-R_{\mathrm {s} }} 631:. Note that these are what would be measured right 136: 16878:McGraw Hill Encyclopaedia of Physics (2nd Edition) 16846: 16785: 16436: 15511: 15183: 14998: 14814: 14718: 14616: 14524: 14443:For the case of normal incidence these reduce to: 14419: 14275: 14109: 13968: 13784: 13641: 13492: 13460: 13399: 13311: 12948: 12595:direction is proportional to the geometric factor 12548: 12332: 12070: 11886: 11349: 11250: 11117: 10970: 10780: 10568: 10330: 9939: 9555: 9456: 9323: 9176: 8986: 8771: 8529: 8160: 7991: 7839: 7673: 7350: 6625: 6537: 6462: 6386: 6332:{\displaystyle n={\sqrt {\epsilon _{\text{rel}}}}} 6331: 6288: 6232: 6165: 6079: 5996: 5930: 5808: 5630: 5514: 5429: 5377: 5328: 5038: 4723:are scalars, known respectively as the (electric) 4703: 4462:component of vibration. The first derivation from 4295: 4170: 4017: 3807: 3682: 3560: 3008: 2977: 2931: 2653: 2412: 2265: 2115: 2065: 1985: 1563: 1120: 994: 814: 533: 450: 364:. Part of the wave is reflected in the direction 169:polarizations incident upon a material interface. 153:) who was the first to understand that light is a 16112:Whittaker, 1910, p. 134; Darrigol, 2012, p. 12605:and inversely proportional to the wave impedance 10033:So, for the incident, reflected, and transmitted 6584: 6205: 6151: 2128:in the direction of an incident or reflected wave 1979: 1557: 1027:We assume that the media are non-magnetic (i.e., 16962: 16927:Reflection and transmittance for two dielectrics 16417:Buchwald, 1989, p. 442; Fresnel, 1866, pp. 16271: 16269: 16179:T. Young, "Chromatics" (written Sep.– Oct. 11726:(ratio of reflected power to incident power) is 4931:, which is the reciprocal of the wave impedance 4305:These formulas are known respectively as 3712:the characteristic impedance). This results in: 16160:Philosophical Transactions of the Royal Society 15207:The power transmissions can then be found from 11720:), taking squared magnitudes, we find that the 11590:respectively (or for p polarization, using the 9743:field is taken to have unit amplitude, we have 8555:interface conditions for electromagnetic fields 5997:{\displaystyle n=c\,{\sqrt {\mu \epsilon }}\,.} 1121:{\displaystyle Z_{i}={\frac {Z_{0}}{n_{i}}}\,,} 34:. For the thin lens and mirror technology, see 16148: 12140:(conservation of energy). In this way we find 11481:Power ratios (reflectivity and transmissivity) 6245:Dividing the second result by the first gives 4955: 2776:. Those underlying equations supply generally 102:) describe the reflection and transmission of 27:Equations of light transmission and reflection 16372: 16266: 16219: 13649:For non-magnetic media we can substitute the 10039:fields, let the respective components in the 6080:{\displaystyle Y={\sqrt {\epsilon /\mu }}\,.} 2654:{\displaystyle R_{\text{p}}=R_{\text{s}}^{2}} 311: 16933:A self-contained first-principles derivation 16811:(4th ed.). Cambridge University Press. 16668:, 4th Ed., New York: McGraw-Hill, 16076:Hecht, 2002, p. 115, eq. (4.43). 16058:Hecht, 2002, p. 115, eq. (4.42). 16040:Hecht, 2002, p. 120, eq. (4.57). 16031:Hecht, 2002, p. 120, eq. (4.56). 12468: 12413: 12252: 12197: 5453:As usual, we drop the time-dependent factor 5215:. This becomes more obvious when the field ( 5071:is the (constant) complex amplitude vector, 2510: 16085:E. Verdet, in Fresnel, 1866, p. 789n. 16001: 15999: 15974: 15972: 13642:{\displaystyle Y={\frac {n}{\,c\mu \,}}\,.} 13503: 11570: ; so, for s polarization, using the 8204:fields (in the above equations) are in the 6931:as the magnitude of the wave vector in the 5958:. Multiplying the last two equations gives 259:components of the incident wave. Since any 114:. They were deduced by French engineer and 16788:The Cambridge Handbook of Physics Formulas 15786:Reflections of signals on conducting lines 14838:The power reflection coefficients become: 13461:{\displaystyle R={1 \over 2}(R_{s}+R_{p})} 13400:{\displaystyle T={1 \over 2}(T_{s}+T_{p})} 11684:by the proper geometric factor, obtaining 8242:form a right-handed orthogonal triad. The 4407:calcite crystal. He later coined the term 189:and a second medium with refractive index 16806: 16770:Learn how and when to remove this message 16484: 16250: 16191:3 (first half, issued February 1818), pp. 15177: 14808: 14413: 14106: 13778: 13761: 13700: 13635: 13631: 13624: 13132: 13118: 13107: 12769: 12755: 12744: 12407: 12400: 12191: 12184: 11343: 11111: 10770: 10749: 10678: 10562: 10288: 10269: 10215: 10196: 10134: 9897: 9835: 9549: 9317: 8976: 8939: 8852: 8765: 8487: 8468: 8414: 8395: 8333: 8118: 8056: 7833: 7719: 7663: 7340: 7310: 7275: 6456: 6452: 6445: 6282: 6160: 6073: 5990: 5979: 5920: 5798: 5620: 5423: 5325: 5321: 4880:, which is the ratio of the amplitude of 4693: 4506:checking that the final polarization was 3887:which does not propagate as a wave (thus 2831:polarization, the reflection coefficient 2406: 1114: 591:that is reflected from the interface the 330:In the diagram on the right, an incident 16005:Born & Wolf, 1970, p. 40, eqs. 15996: 15969: 12120:in the direction normal to the interface 6642: 2818: 2810: 578: 570: 321: 246: 236: 229:. The incident light is assumed to be a 40: 16575:, 4th Ed., Oxford: Pergamon Press. 16280:767–99 (full text, published 1831), pp. 16125: 15538: 6387:{\textstyle Z={\sqrt {\mu /\epsilon }}} 5125:is time, and it is understood that the 4892:. It is therefore desirable to express 4180:If we do likewise with the formula for 2851:field amplitudes (or equivalently, the 326:Variables used in the Fresnel equations 14: 16963: 16868:Encyclopaedia of Physics (2nd Edition) 16844: 16425:749. Cf. Whewell, 1857, pp. 7913:, respectively. Then, if the incident 6949:), then the wave vector has magnitude 6300:medium (the usual case), this becomes 4593: 3009:{\displaystyle \theta _{\mathrm {t} }} 2932:{\displaystyle \theta _{\mathrm {i} }} 370:, and part refracted in the direction 16595:Foundations for Microwave Engineering 16429:356–8; Jenkins & White, 1976, pp. 15386:which is zero (by Snell's law). Hence 15325:, so that the numerator in equation ( 15220: 13588: 587:We call the fraction of the incident 16825: 16783: 16726: 16718:, London: Longmans, Green, & Co. 16621:Oeuvres complètes d'Augustin Fresnel 16529:"Brewster angles for magnetic media" 16408:230–31; Fresnel, 1866, p. 744. 16393:Bulletin de la Société philomathique 15449: 15021: 14840: 14741: 14639: 14547: 14445: 14298: 14132: 13991: 13825: 12974: 12611: 12358: 12142: 11912: 11728: 11276: 11171: 10996: 10827: 10612: 10368: 10366:fields must be continuous; that is, 10103: 9745: 9482: 9377: 9202: 9033: 8815: 8571: 8569:fields must be continuous; that is, 8302: 8017: 7933: 7699: 7370: 6042: 5960: 5466: 5393: 4975: 4844:is indeed very close to 1; that is, 4753:, respectively. Hence we define the 4333: 3931: 2873:are generally different between the 2823:Amplitude coefficients: glass to air 2815:Amplitude coefficients: air to glass 2130:(given by the magnitude of a wave's 16664:F.A. Jenkins and H.E. White, 1976, 16356:792–6; Whewell, 1857, p. 359. 15936:Encyclopedia of Optical Engineering 15810:) is typically used by physicists. 11647:in a medium of intrinsic impedance 10592:When we substitute from equations ( 9664: 8795:When we substitute from equations ( 8557:, the tangential components of the 7863: 5300: must increase at the velocity 2445: 2291: 24: 16722: 16450:50, Amsterdam: Elsevier, 2007, pp. 15447:in Snell's law, we readily obtain 11677:or, equivalently, simply multiply 6694:to a medium with refractive index 6453: 3000: 2986:, and a wave transmitted at angle 2969: 2954: 2923: 2847:is the ratio of the waves complex 2249: 2234: 2204: 2201: 2198: 2107: 2086: 2057: 2036: 1960: 1916: 1848: 1804: 1714: 1683: 1653: 1622: 1583: 1525: 1456: 1413: 1344: 1292: 1261: 1231: 1200: 1161: 970: 939: 909: 878: 839: 790: 759: 729: 698: 659: 522: 491: 439: 424: 25: 17007: 16891: 15814:typically prefer the form 6396:In a vacuum this takes the value 4860:In optics, one usually knows the 3638:is just the squared magnitude of 16948: 16731: 16227:Annales de Chimie et de Physique 16170:125–59, read 16 March 1815. 16128:Optical Properties of Thin Films 11661:component (rather than the full 10315: 10301: 10242: 10228: 10169: 10155: 9924: 9910: 9862: 9848: 9800: 9786: 8514: 8500: 8441: 8427: 8368: 8354: 8145: 8131: 8083: 8069: 7980: 7966: 7794: 7780: 7771: 7757: 7748: 7734: 7582: 7568: 7491: 7477: 7400: 7386: 7306: 7271: 7231: 7207: 7173: 7144: 7120: 7086: 7057: 7033: 6999: 6805:plane is the interface, and the 5794: 5786: 5771: 5756: 5748: 5736: 5616: 5608: 5593: 5581: 5573: 5561: 5503: 5497: 5482: 5478: 5135:varies in a direction normal to 5015: 5009: 4991: 4987: 4689: 4674: 4665: 4650: 4403:of the two rays emerging from a 2889:do not even apply!) the sign of 2586: 2456:At a dielectric interface from 2286: 1024:of media 1 and 2, respectively. 575:Power coefficients: air to glass 317: 123: 62: 53: 16809:Introduction to Electrodynamics 16582:, University of Chicago Press, 16550: 16521: 16478: 16469: 16411: 16398: 16359: 16342: 16317: 16308: 16291: 16202: 16173: 16135: 16119: 16106: 16097: 16088: 16079: 16070: 16061: 16052: 16043: 16018:Hecht, 2002, p. 116, eqs. 15978:Lecture notes by Bo Sernelius, 15863: 15798: 15212: = 1 −  8553:At the interface, by the usual 6638: 5430:{\displaystyle k=n\omega /c\,.} 16971:Eponymous equations of physics 16792:. Cambridge University Press. 16034: 16025: 16012: 15960: 15927: 15918: 15909: 15506: 15478: 13455: 13429: 13394: 13368: 7660: 7596: 7559: 7515: 7468: 7424: 7337: 7267: 7251: 7203: 7164: 7116: 7077: 7029: 6974:in the diagram) and magnitude 6351:), we find that the intrinsic 6116:) we obtain the phase velocity 5546:respectively reduce to 5329:{\displaystyle \omega /k\,,\,} 5028: 5005: 4960:In a uniform plane sinusoidal 4284: 4258: 4247: 4221: 4159: 4133: 4122: 4096: 3815:using the above definition of 3795: 3786: 3667: 3658: 623:power transmission coefficient 559:coefficients, since power (or 380:of the interface are given as 13: 1: 16754:and help improve the section. 16460:10.1016/S0079-6638(07)50002-8 16314:Buchwald, 1989, p. 392. 15915:Born & Wolf, 1970, p. 38. 15902: 15716:and that the vibrations were 15696:and that the vibrations were 12562: 12346: 8192:polarization, that means the 6827:) be the unit vectors in the 5853:right-handed orthogonal triad 4585: 3875:where the power transmission 2541:, all light is reflected and 16904:Fresnel equations calculator 16615:A. Fresnel, 1866 (ed. 16067:Fresnel, 1866, p. 757. 16049:Fresnel, 1866, p. 773. 15700:to what was then called the 15688: 15639: 15615: 15609: 15588: 15582: 15525: 15327: 15197: 15012: 14828: 14732: 14630: 14538: 14433: 14289: 14123: 13982: 13812: 13806: 13800: 13794: 13577: 13571: 13565: 13559: 13553: 13547: 13325: 12972:for the s polarization, and 12962: 12587: 12581: 12356:for the s polarization, and 12084: 11910:for the s polarization, and 11900: 11716: 11710: 11464: 11458: 11452: 11446: 11363: 11264: 11131: 10984: 10794: 10600: 10594: 10582: 10344: 9953: 9569: 9470: 9337: 9190: 9010:which are easily solved for 9000: 8803: 8785: 8543: 6178:For a vacuum this reduces to 5706:to obtain equations in only 4564:, and in which he explained 3926:polarization transformations 2940:, a wave reflected at angle 2772:shifts in addition to their 2558:. This phenomenon, known as 639:transmission or reflection. 603:power reflection coefficient 334:in the direction of the ray 292:the plane of incidence (the 7: 16853:. Oxford University Press. 16653:, 4th Ed., Addison Wesley, 16638:, 2nd Ed., Addison Wesley, 16569:M. Born and E. Wolf, 1970, 16327:369–70; Buchwald, 1989, pp. 16301:391–3; Whittaker, 1910, pp. 15828:that is, they not only use 15806: 15723: 15552: 15546: 13601: 13595: 13516: 13510: 10606: 8809: 8797: 8174: 8005: 7921: 7853: 7687: 7364: 6961:in the first medium (region 6911: 6347: 6112: 6093: 6010: 5857: 5816:If the material parameters 5694:as above, we can eliminate 5528: 5443: 5290:. If the argument of 5270: 5217: 5148:is normal to the wavefronts 5052: 4956:Electromagnetic plane waves 4364:Fabry–Pérot interferometers 3821:. The introduced factor of 2181:polarizations, so that the 552: 172: 10: 17012: 16563: 16395:for 1822, pp. 191–8). 16212:390–91; Fresnel, 1866, pp. 15966:Hecht, 1987, p. 102. 15745:Field and power quantities 6759:, etc., and let the region 6345:Taking the reciprocal of ( 5353:. This in turn is equal to 4452:French Academy of Sciences 4388: 4384: 3683:{\displaystyle R=|r|^{2}.} 2514: 2449: 822:while the reflectance for 240: 29: 16830:. John Wiley & Sons. 10017:field in the case of the 7882:field is parallel to the 6707:In Cartesian coordinates 5538:For fields of that form, 5296:is to be constant, 3936:In the above formula for 3873:total internal reflection 2560:total internal reflection 2517:Total internal reflection 2511:Total internal reflection 108:electromagnetic radiation 15791: 15704:, or by supposing (like 13504:Equal refractive indices 12572:for the p polarization. 9737:. Then, if the incident 4610:, the four field vectors 4606:. If the medium is also 4541:complex refractive index 4466:principles was given by 4437:transverse elastic waves 4064:, we obtain 3706:characteristic impedance 2487:, and is around 56° for 2010:trigonometric identities 314:in which that is true). 16487:Applied Physics Letters 16383:731–51 (full text), pp. 16335:453; Fresnel, 1866, pp. 16126:Heavens, O. S. (1955). 15766:Schlick's approximation 15740:Index-matching material 15619:), the expressions for 13345:For unpolarized light: 10025:. The agreement of the 6789:, intrinsic admittance 6749:, intrinsic admittance 6475:impedance of free space 4914:, and thence to relate 4561:elliptical polarization 4368:antireflection coatings 3031:Using this convention, 2281:Schlick's approximation 2141:for a wave at an angle 1139:impedance of free space 16845:Kenyon, I. R. (2008). 16666:Fundamentals of Optics 16261:10.5281/zenodo.4058004 15535:for Brewster's angle. 15513: 15185: 15000: 14816: 14720: 14618: 14526: 14421: 14277: 14111: 13970: 13786: 13643: 13494: 13462: 13401: 13313: 12950: 12550: 12334: 12072: 11888: 11351: 11252: 11119: 10972: 10782: 10570: 10332: 10001:fields must be in the 9941: 9557: 9458: 9325: 9178: 8988: 8773: 8531: 8162: 7993: 7841: 7675: 7352: 6878:, where the subscript 6779:have refractive index 6739:have refractive index 6704: 6627: 6539: 6464: 6388: 6333: 6290: 6234: 6167: 6081: 5998: 5946:are the magnitudes of 5932: 5810: 5632: 5516: 5431: 5379: 5330: 5040: 4705: 4521:Fresnel rhomb § 4429: 4379:transfer-matrix method 4297: 4172: 4019: 3809: 3684: 3562: 3010: 2979: 2933: 2824: 2816: 2655: 2414: 2267: 2117: 2067: 2017:conservation of energy 1987: 1565: 1122: 996: 816: 584: 576: 535: 452: 327: 252: 46: 16880:, C.B. Parker, 1994, 16597:, Tokyo: McGraw-Hill. 16578:J.Z. Buchwald, 1989, 16462:, at p. 18, eq. 16391:, first published in 16022:(4.49), (4.50). 15702:plane of polarization 15514: 15186: 15001: 14817: 14721: 14619: 14527: 14422: 14278: 14112: 13971: 13787: 13644: 13495: 13493:{\displaystyle R+T=1} 13463: 13402: 13314: 12951: 12551: 12335: 12126:direction) is to use 12073: 11889: 11352: 11253: 11120: 10973: 10783: 10571: 10333: 9942: 9558: 9459: 9326: 9179: 8989: 8774: 8532: 8163: 7994: 7842: 7676: 7353: 6646: 6628: 6554:medium, this becomes 6540: 6465: 6389: 6334: 6291: 6235: 6168: 6082: 5999: 5933: 5811: 5633: 5517: 5432: 5380: 5331: 5180:(that is, we replace 5041: 4706: 4579:Augustin-Jean Fresnel 4555:circular polarization 4537:Augustin-Louis Cauchy 4441:plane of polarization 4433:Augustin-Jean Fresnel 4425: 4391:Augustin-Jean Fresnel 4389:Further information: 4311:Fresnel's tangent law 4298: 4173: 4020: 3810: 3685: 3563: 3011: 2980: 2934: 2822: 2814: 2763:electromagnetic field 2656: 2607:equals the square of 2432:) surrounded by air ( 2415: 2268: 2118: 2068: 1988: 1566: 1123: 997: 817: 582: 574: 536: 453: 325: 250: 237:S and P polarizations 119:Augustin-Jean Fresnel 44: 16991:Polarization (waves) 16826:Band, Y. B. (2010). 16572:Principles of Optics 16365:Whittaker, 1910, pp. 15924:Hecht, 1987, p. 100. 15812:Electrical engineers 15562:is fixed instead of 15539:Equal permittivities 15456: 15028: 14847: 14748: 14646: 14554: 14452: 14305: 14139: 13998: 13832: 13671: 13609: 13472: 13410: 13349: 12981: 12618: 12365: 12149: 11919: 11735: 11614:in the direction of 11283: 11178: 11003: 10834: 10619: 10375: 10110: 9752: 9489: 9384: 9209: 9040: 8822: 8578: 8309: 8024: 7940: 7707: 7377: 7362:in the phasor form ( 6990: 6558: 6482: 6400: 6360: 6306: 6249: 6186: 6124: 6105:intrinsic admittance 6049: 5967: 5865: 5722: 5550: 5473: 5400: 5361: 5307: 5259:in the direction of 5253:is the component of 4982: 4962:electromagnetic wave 4886:to the amplitude of 4642: 4423:was moved to write: 4196: 4068: 3952: 3716: 3648: 3035: 2991: 2945: 2914: 2768:, i.e., considering 2620: 2321: 2189: 2077: 2027: 2015:As a consequence of 1574: 1152: 1074: 830: 650: 642:The reflectance for 545:electromagnetic wave 466: 415: 100:Fresnel coefficients 82:Polarized sunglasses 16600:O. Darrigol, 2012, 16593:R.E. Collin, 1966, 16543:3 (March 1985), pp. 16499:1982ApPhL..40..210G 16404:Buchwald, 1989, pp. 16297:Buchwald, 1989, pp. 16208:Buchwald, 1989, pp. 16197:concluding sentence 16141:Darrigol, 2012, pp. 15761:Specular reflection 15735:Polarization mixing 15249:, we can substitute 13651:vacuum permeability 11620:is given simply by 10081:. Then, since 8284:. Then, since 5378:{\displaystyle c/n} 4759:dielectric constant 4729:and the (magnetic) 4594:Material parameters 4549:linear polarization 4397:Étienne-Louis Malus 3026:inhomogeneous waves 2650: 32:Fresnel diffraction 16996:History of physics 16981:Geometrical optics 16694:W. Whewell, 1857, 16444:Progress in Optics 16348:Fresnel, 1866, pp. 15985:2012-02-22 at the 15781:Plane of incidence 15776:X-ray reflectivity 15509: 15181: 14996: 14812: 14716: 14614: 14522: 14417: 14273: 14107: 13966: 13782: 13639: 13589:Non-magnetic media 13490: 13458: 13397: 13309: 12946: 12546: 12330: 12068: 11884: 11468:), we see that at 11347: 11248: 11115: 10968: 10778: 10776: 10566: 10520: 10328: 10326: 10045: direction be 9937: 9935: 9553: 9454: 9321: 9174: 8984: 8982: 8769: 8723: 8527: 8525: 8158: 8156: 7989: 7876:polarization, the 7837: 7671: 7669: 7348: 7346: 6935:medium (for which 6901:In the absence of 6705: 6623: 6535: 6460: 6384: 6329: 6286: 6230: 6163: 6077: 5994: 5928: 5926: 5806: 5804: 5628: 5626: 5544:Maxwell-Ampère law 5512: 5427: 5375: 5326: 5036: 4701: 4699: 4431:In 1821, however, 4358:colours seen in a 4307:Fresnel's sine law 4293: 4168: 4015: 3805: 3680: 3558: 3556: 3006: 2975: 2929: 2908:angle of incidence 2825: 2817: 2766:complex amplitudes 2651: 2636: 2576:). For glass with 2422:For common glass ( 2410: 2263: 2113: 2063: 1983: 1561: 1118: 992: 812: 585: 577: 547:, and the laws of 531: 448: 328: 278:plane of incidence 261:polarization state 253: 243:Plane of incidence 222:at the interface. 47: 18:Fresnel reflection 16898:Fresnel Equations 16860:978-0-19-856646-5 16837:978-0-471-89931-0 16818:978-1-108-42041-9 16799:978-0-521-57507-2 16784:Woan, G. (2010). 16780: 16779: 16772: 16610:978-0-19-964437-7 16130:. Academic Press. 16009:(20), (21). 15989:, see especially 15953:978-0-8247-0940-2 15842:complex conjugate 15533: 15532: 15466: 15205: 15204: 15165: 15161: 15132: 15104: 15075: 15038: 15020: 15019: 14984: 14980: 14951: 14923: 14894: 14857: 14836: 14835: 14806: 14758: 14740: 14739: 14714: 14656: 14638: 14637: 14612: 14564: 14546: 14545: 14520: 14462: 14441: 14440: 14411: 14407: 14378: 14350: 14315: 14297: 14296: 14271: 14267: 14238: 14210: 14181: 14149: 14131: 14130: 14104: 14100: 14071: 14043: 14008: 13990: 13989: 13964: 13960: 13931: 13903: 13874: 13842: 13804:) and equations ( 13776: 13734: 13731: 13728: 13722: 13719: 13715: 13633: 13427: 13366: 13333: 13332: 13307: 13293: 13264: 13231: 13215: 13171: 13167: 13149: 13130: 13092: 13088: 13059: 13031: 12991: 12970: 12969: 12944: 12930: 12901: 12868: 12852: 12808: 12804: 12786: 12767: 12729: 12725: 12696: 12668: 12628: 12570: 12569: 12544: 12530: 12501: 12465: 12449: 12411: 12394: 12375: 12354: 12353: 12328: 12314: 12285: 12249: 12233: 12195: 12178: 12159: 12092: 12091: 12056: 12052: 12023: 11995: 11966: 11929: 11908: 11907: 11872: 11868: 11839: 11811: 11782: 11745: 11700: cos  11652: = 1/ 11376:grazing incidence 11371: 11370: 11341: 11293: 11272: 11271: 11246: 11188: 11139: 11138: 11109: 11105: 11076: 11048: 11013: 10992: 10991: 10966: 10962: 10933: 10905: 10876: 10844: 10802: 10801: 10767: 10739: 10702: 10686: 10668: 10652: 10639: 10604:) and then from ( 10590: 10589: 10552: 10549: 10545: 10541: 10538: 10535: 10527: 10524: 10515: 10498: 10485: 10471: 10455: 10438: 10422: 10409: 10393: 10352: 10351: 10308: 10259: 10235: 10186: 10162: 10124: 9961: 9960: 9917: 9879: 9855: 9817: 9793: 9766: 9581:grazing incidence 9577: 9576: 9547: 9499: 9478: 9477: 9452: 9394: 9345: 9344: 9315: 9311: 9282: 9254: 9219: 9198: 9197: 9172: 9168: 9139: 9111: 9082: 9050: 9008: 9007: 8973: 8957: 8929: 8913: 8890: 8860: 8842: 8807:) and then from ( 8793: 8792: 8755: 8752: 8748: 8744: 8741: 8738: 8730: 8727: 8718: 8702: 8685: 8669: 8656: 8640: 8626: 8609: 8596: 8551: 8550: 8507: 8458: 8434: 8385: 8361: 8323: 8182: 8181: 8138: 8100: 8076: 8038: 8013: 8012: 7973: 7950: 7861: 7860: 7830: 7787: 7764: 7741: 7731: 7728: 7725: 7695: 7694: 7657: 7625: 7575: 7556: 7534: 7484: 7465: 7443: 7393: 7334: 7299: 7248: 7224: 7180: 7161: 7137: 7093: 7074: 7050: 7006: 6597: 6594: 6533: 6530: 6515: 6443: 6382: 6327: 6324: 6280: 6277: 6267: 6228: 6161: 6101: 6100: 6071: 6018: 6017: 5988: 5536: 5535: 5451: 5450: 5117:angular frequency 5091:(whose magnitude 5060: 5059: 4781: , and the 4757:permittivity (or 4421:Thomas Young 4405:doubly-refractive 4334:Multiple surfaces 4288: 4281: 4268: 4244: 4231: 4206: 4163: 4156: 4143: 4119: 4106: 4078: 4012: 3991: 3932:Alternative forms 3783: 3779: 3751: 3570:One can see that 3549: 3545: 3516: 3488: 3449: 3433: 3429: 3400: 3372: 3343: 3307: 3291: 3287: 3258: 3230: 3191: 3175: 3171: 3142: 3114: 3085: 3049: 2643: 2630: 2507:(typical glass). 2394: 2277:computer graphics 2221: 1967: 1933: 1902: 1821: 1790: 1721: 1545: 1542: 1511: 1430: 1399: 1299: 1112: 977: 824:p-polarized light 797: 644:s-polarized light 409:law of reflection 96:Fresnel equations 16:(Redirected from 17003: 16953: 16952: 16944: 16864: 16852: 16841: 16822: 16803: 16791: 16775: 16768: 16764: 16761: 16755: 16750:Please read the 16746:may need cleanup 16735: 16734: 16727: 16703: 16690: 16679:H. Lloyd, 1834, 16649:E. Hecht, 2002, 16634:E. Hecht, 1987, 16628: 16618: 16557: 16554: 16548: 16546: 16542: 16538: 16525: 16519: 16518: 16482: 16476: 16473: 16467: 16465: 16453: 16449: 16440: 16434: 16432: 16428: 16424: 16420: 16415: 16409: 16407: 16402: 16396: 16386: 16382: 16376: 16370: 16368: 16363: 16357: 16355: 16351: 16346: 16340: 16338: 16334: 16330: 16326: 16323:Lloyd, 1834, pp. 16321: 16315: 16312: 16306: 16304: 16300: 16295: 16289: 16287: 16283: 16279: 16273: 16264: 16254: 16244: 16240: 16236: 16232: 16223: 16217: 16215: 16211: 16206: 16200: 16194: 16190: 16182: 16177: 16171: 16169: 16165: 16152: 16146: 16144: 16139: 16133: 16131: 16123: 16117: 16115: 16110: 16104: 16101: 16095: 16092: 16086: 16083: 16077: 16074: 16068: 16065: 16059: 16056: 16050: 16047: 16041: 16038: 16032: 16029: 16023: 16021: 16016: 16010: 16008: 16003: 15994: 15976: 15967: 15964: 15958: 15957: 15931: 15925: 15922: 15916: 15913: 15896: 15894: 15888: 15877: 15875: 15867: 15861: 15859: 15853: 15847: 15839: 15833: 15827: 15804:The above form ( 15802: 15681: 15677: 15676: 15665: 15661: 15658: 15656: 15646: 15636: 15627: 15606: 15579: 15576:proportional to 15571: 15567: 15561: 15527: 15518: 15516: 15515: 15510: 15505: 15504: 15495: 15490: 15489: 15468: 15467: 15464: 15450: 15446: 15443: 15436: 15431: 15427: 15424: 15417: 15412: 15404: 15401: 15399: 15389: 15385: 15381: 15380: 15371: 15367: 15357: 15348: 15344: 15334: 15324: 15323: 15314: 15309: 15305: 15302: 15295: 15290: 15286: 15285: 15276: 15271: 15267: 15264: 15257: 15252: 15242: 15233: 15221:Brewster's angle 15216: 15199: 15190: 15188: 15187: 15182: 15176: 15175: 15170: 15166: 15164: 15163: 15162: 15159: 15147: 15146: 15134: 15133: 15130: 15118: 15117: 15107: 15106: 15105: 15102: 15090: 15089: 15077: 15076: 15073: 15061: 15060: 15050: 15040: 15039: 15036: 15022: 15014: 15005: 15003: 15002: 14997: 14995: 14994: 14989: 14985: 14983: 14982: 14981: 14978: 14966: 14965: 14953: 14952: 14949: 14937: 14936: 14926: 14925: 14924: 14921: 14909: 14908: 14896: 14895: 14892: 14880: 14879: 14869: 14859: 14858: 14855: 14841: 14830: 14821: 14819: 14818: 14813: 14807: 14805: 14804: 14803: 14791: 14790: 14780: 14779: 14778: 14765: 14760: 14759: 14756: 14742: 14734: 14725: 14723: 14722: 14717: 14715: 14713: 14712: 14711: 14699: 14698: 14688: 14687: 14686: 14674: 14673: 14663: 14658: 14657: 14654: 14640: 14632: 14623: 14621: 14620: 14615: 14613: 14611: 14610: 14609: 14597: 14596: 14586: 14585: 14584: 14571: 14566: 14565: 14562: 14548: 14540: 14531: 14529: 14528: 14523: 14521: 14519: 14518: 14517: 14505: 14504: 14494: 14493: 14492: 14480: 14479: 14469: 14464: 14463: 14460: 14446: 14435: 14426: 14424: 14423: 14418: 14412: 14410: 14409: 14408: 14405: 14393: 14392: 14380: 14379: 14376: 14364: 14363: 14353: 14352: 14351: 14348: 14336: 14335: 14322: 14317: 14316: 14313: 14299: 14291: 14282: 14280: 14279: 14274: 14272: 14270: 14269: 14268: 14265: 14253: 14252: 14240: 14239: 14236: 14224: 14223: 14213: 14212: 14211: 14208: 14196: 14195: 14183: 14182: 14179: 14167: 14166: 14156: 14151: 14150: 14147: 14133: 14125: 14116: 14114: 14113: 14108: 14105: 14103: 14102: 14101: 14098: 14086: 14085: 14073: 14072: 14069: 14057: 14056: 14046: 14045: 14044: 14041: 14029: 14028: 14015: 14010: 14009: 14006: 13992: 13984: 13975: 13973: 13972: 13967: 13965: 13963: 13962: 13961: 13958: 13946: 13945: 13933: 13932: 13929: 13917: 13916: 13906: 13905: 13904: 13901: 13889: 13888: 13876: 13875: 13872: 13860: 13859: 13849: 13844: 13843: 13840: 13826: 13791: 13789: 13788: 13783: 13777: 13775: 13774: 13773: 13759: 13758: 13749: 13744: 13743: 13732: 13729: 13726: 13720: 13717: 13716: 13714: 13713: 13712: 13698: 13697: 13688: 13683: 13682: 13666: 13660: 13648: 13646: 13645: 13640: 13634: 13632: 13619: 13544: 13541: 13533: 13523: 13508:From equations ( 13499: 13497: 13496: 13491: 13467: 13465: 13464: 13459: 13454: 13453: 13441: 13440: 13428: 13420: 13406: 13404: 13403: 13398: 13393: 13392: 13380: 13379: 13367: 13359: 13341: 13340: = 0 13327: 13318: 13316: 13315: 13310: 13308: 13306: 13305: 13300: 13296: 13295: 13294: 13291: 13279: 13278: 13266: 13265: 13262: 13250: 13249: 13234: 13233: 13232: 13229: 13217: 13216: 13213: 13201: 13200: 13191: 13190: 13177: 13172: 13170: 13169: 13168: 13165: 13152: 13151: 13150: 13147: 13134: 13131: 13129: 13128: 13119: 13117: 13116: 13105: 13103: 13102: 13097: 13093: 13091: 13090: 13089: 13086: 13074: 13073: 13061: 13060: 13057: 13045: 13044: 13034: 13033: 13032: 13029: 13017: 13016: 13003: 12993: 12992: 12989: 12975: 12964: 12955: 12953: 12952: 12947: 12945: 12943: 12942: 12937: 12933: 12932: 12931: 12928: 12916: 12915: 12903: 12902: 12899: 12887: 12886: 12871: 12870: 12869: 12866: 12854: 12853: 12850: 12838: 12837: 12828: 12827: 12814: 12809: 12807: 12806: 12805: 12802: 12789: 12788: 12787: 12784: 12771: 12768: 12766: 12765: 12756: 12754: 12753: 12742: 12740: 12739: 12734: 12730: 12728: 12727: 12726: 12723: 12711: 12710: 12698: 12697: 12694: 12682: 12681: 12671: 12670: 12669: 12666: 12654: 12653: 12640: 12630: 12629: 12626: 12612: 12608: 12604: 12603: 12594: 12564: 12555: 12553: 12552: 12547: 12545: 12543: 12542: 12537: 12533: 12532: 12531: 12528: 12516: 12515: 12503: 12502: 12499: 12487: 12486: 12471: 12467: 12466: 12463: 12451: 12450: 12447: 12435: 12434: 12425: 12424: 12412: 12409: 12402: 12396: 12395: 12392: 12377: 12376: 12373: 12359: 12348: 12339: 12337: 12336: 12331: 12329: 12327: 12326: 12321: 12317: 12316: 12315: 12312: 12300: 12299: 12287: 12286: 12283: 12271: 12270: 12255: 12251: 12250: 12247: 12235: 12234: 12231: 12219: 12218: 12209: 12208: 12196: 12193: 12186: 12180: 12179: 12176: 12161: 12160: 12157: 12143: 12139: 12136: 12135: = 1 12125: 12101: 12097: 12086: 12077: 12075: 12074: 12069: 12067: 12066: 12061: 12057: 12055: 12054: 12053: 12050: 12038: 12037: 12025: 12024: 12021: 12009: 12008: 11998: 11997: 11996: 11993: 11981: 11980: 11968: 11967: 11964: 11952: 11951: 11941: 11931: 11930: 11927: 11913: 11902: 11893: 11891: 11890: 11885: 11883: 11882: 11877: 11873: 11871: 11870: 11869: 11866: 11854: 11853: 11841: 11840: 11837: 11825: 11824: 11814: 11813: 11812: 11809: 11797: 11796: 11784: 11783: 11780: 11768: 11767: 11757: 11747: 11746: 11743: 11729: 11708:From equations ( 11704: 11699: 11688: 11683: 11676: 11670: 11664: 11660: 11656: 11646: 11643: 11634: 11630: 11626: 11619: 11609: 11603: 11597: 11593: 11589: 11583: 11577: 11573: 11569: 11563: 11557: 11547: 11541: 11535: 11530: 11526: 11519: 11516: 11514: 11513: 11510: 11507: 11500: 11440: 11431: 11427: 11424: 11415: 11411: 11410: 11400: 11395: 11391: 11389: 11378: 11365: 11356: 11354: 11353: 11348: 11342: 11340: 11339: 11338: 11326: 11325: 11315: 11314: 11313: 11300: 11295: 11294: 11291: 11277: 11266: 11257: 11255: 11254: 11249: 11247: 11245: 11244: 11243: 11231: 11230: 11220: 11219: 11218: 11206: 11205: 11195: 11190: 11189: 11186: 11172: 11168: 11164: 11157: 11147: 11143:normal incidence 11133: 11124: 11122: 11121: 11116: 11110: 11108: 11107: 11106: 11103: 11091: 11090: 11078: 11077: 11074: 11062: 11061: 11051: 11050: 11049: 11046: 11034: 11033: 11020: 11015: 11014: 11011: 10997: 10986: 10977: 10975: 10974: 10969: 10967: 10965: 10964: 10963: 10960: 10948: 10947: 10935: 10934: 10931: 10919: 10918: 10908: 10907: 10906: 10903: 10891: 10890: 10878: 10877: 10874: 10862: 10861: 10851: 10846: 10845: 10842: 10828: 10824: 10823: 10812: 10796: 10787: 10785: 10784: 10779: 10777: 10769: 10768: 10765: 10759: 10758: 10741: 10740: 10737: 10731: 10730: 10718: 10717: 10704: 10703: 10700: 10688: 10687: 10684: 10670: 10669: 10666: 10654: 10653: 10650: 10641: 10640: 10637: 10613: 10584: 10575: 10573: 10572: 10567: 10550: 10547: 10546: 10543: 10539: 10536: 10533: 10532: 10528: 10525: 10522: 10521: 10517: 10516: 10513: 10500: 10499: 10496: 10487: 10486: 10483: 10473: 10472: 10469: 10457: 10456: 10453: 10440: 10439: 10436: 10424: 10423: 10420: 10411: 10410: 10407: 10395: 10394: 10391: 10369: 10365: 10359: 10346: 10337: 10335: 10334: 10329: 10327: 10320: 10319: 10318: 10310: 10309: 10306: 10304: 10290: 10289: 10279: 10278: 10261: 10260: 10257: 10247: 10246: 10245: 10237: 10236: 10233: 10231: 10217: 10216: 10206: 10205: 10188: 10187: 10184: 10174: 10173: 10172: 10164: 10163: 10160: 10158: 10144: 10143: 10126: 10125: 10122: 10104: 10100: 10099: 10094: 10090: 10084: 10080: 10072: 10068: 10059: 10048: 10044: 10038: 10024: 10016: 10010: 10006: 10000: 9994: 9991: 9987: 9980: 9972: 9968: 9955: 9946: 9944: 9943: 9938: 9936: 9929: 9928: 9927: 9919: 9918: 9915: 9913: 9899: 9898: 9881: 9880: 9877: 9867: 9866: 9865: 9857: 9856: 9853: 9851: 9837: 9836: 9819: 9818: 9815: 9805: 9804: 9803: 9795: 9794: 9791: 9789: 9768: 9767: 9764: 9746: 9742: 9736: 9727: 9718: 9710: 9706: 9697: 9686: 9682: 9660: 9658: 9648: 9644: 9641: 9639: 9635: 9625: 9621: 9620: 9616: 9607: 9602: 9598: 9596: 9585: 9571: 9562: 9560: 9559: 9554: 9548: 9546: 9545: 9544: 9532: 9531: 9521: 9520: 9519: 9506: 9501: 9500: 9497: 9483: 9472: 9463: 9461: 9460: 9455: 9453: 9451: 9450: 9449: 9437: 9436: 9426: 9425: 9424: 9412: 9411: 9401: 9396: 9395: 9392: 9378: 9374: 9370: 9363: 9353: 9349:normal incidence 9339: 9330: 9328: 9327: 9322: 9316: 9314: 9313: 9312: 9309: 9297: 9296: 9284: 9283: 9280: 9268: 9267: 9257: 9256: 9255: 9252: 9240: 9239: 9226: 9221: 9220: 9217: 9203: 9192: 9183: 9181: 9180: 9175: 9173: 9171: 9170: 9169: 9166: 9154: 9153: 9141: 9140: 9137: 9125: 9124: 9114: 9113: 9112: 9109: 9097: 9096: 9084: 9083: 9080: 9068: 9067: 9057: 9052: 9051: 9048: 9034: 9030: 9029: 9018: 9002: 8993: 8991: 8990: 8985: 8983: 8975: 8974: 8971: 8959: 8958: 8955: 8949: 8948: 8931: 8930: 8927: 8915: 8914: 8911: 8905: 8904: 8892: 8891: 8888: 8876: 8875: 8862: 8861: 8858: 8844: 8843: 8840: 8816: 8787: 8778: 8776: 8775: 8770: 8753: 8750: 8749: 8746: 8742: 8739: 8736: 8735: 8731: 8728: 8725: 8724: 8720: 8719: 8716: 8704: 8703: 8700: 8687: 8686: 8683: 8671: 8670: 8667: 8658: 8657: 8654: 8642: 8641: 8638: 8628: 8627: 8624: 8611: 8610: 8607: 8598: 8597: 8594: 8572: 8568: 8562: 8545: 8536: 8534: 8533: 8528: 8526: 8519: 8518: 8517: 8509: 8508: 8505: 8503: 8489: 8488: 8478: 8477: 8460: 8459: 8456: 8446: 8445: 8444: 8436: 8435: 8432: 8430: 8416: 8415: 8405: 8404: 8387: 8386: 8383: 8373: 8372: 8371: 8363: 8362: 8359: 8357: 8343: 8342: 8325: 8324: 8321: 8303: 8299: 8298: 8287: 8283: 8275: 8271: 8262: 8251: 8247: 8241: 8238: 8234: 8227: 8219: 8215: 8209: 8203: 8197: 8176: 8167: 8165: 8164: 8159: 8157: 8150: 8149: 8148: 8140: 8139: 8136: 8134: 8120: 8119: 8102: 8101: 8098: 8088: 8087: 8086: 8078: 8077: 8074: 8072: 8058: 8057: 8040: 8039: 8036: 8018: 8007: 7998: 7996: 7995: 7990: 7985: 7984: 7983: 7975: 7974: 7971: 7969: 7952: 7951: 7948: 7934: 7930: 7918: 7912: 7902: 7893: 7887: 7881: 7855: 7846: 7844: 7843: 7838: 7832: 7831: 7828: 7810: 7809: 7797: 7789: 7788: 7785: 7783: 7774: 7766: 7765: 7762: 7760: 7751: 7743: 7742: 7739: 7737: 7729: 7726: 7723: 7700: 7689: 7680: 7678: 7677: 7672: 7670: 7659: 7658: 7655: 7640: 7639: 7627: 7626: 7623: 7608: 7607: 7585: 7577: 7576: 7573: 7571: 7558: 7557: 7554: 7536: 7535: 7532: 7511: 7510: 7494: 7486: 7485: 7482: 7480: 7467: 7466: 7463: 7445: 7444: 7441: 7420: 7419: 7403: 7395: 7394: 7391: 7389: 7371: 7357: 7355: 7354: 7349: 7347: 7336: 7335: 7332: 7320: 7319: 7309: 7301: 7300: 7297: 7285: 7284: 7274: 7257: 7250: 7249: 7246: 7234: 7226: 7225: 7222: 7210: 7199: 7198: 7182: 7181: 7178: 7176: 7163: 7162: 7159: 7147: 7139: 7138: 7135: 7123: 7112: 7111: 7095: 7094: 7091: 7089: 7076: 7075: 7072: 7060: 7052: 7051: 7048: 7036: 7025: 7024: 7008: 7007: 7004: 7002: 6985: 6973: 6970: 6964: 6960: 6948: 6946: 6942: 6930: 6923: 6918:So, for a given 6893: 6883: 6877: 6876: 6865: 6859: 6853: 6844: 6838: 6832: 6822: 6816: 6810: 6804: 6799:, etc. Then the 6798: 6788: 6778: 6775: 6773: 6769: 6762: 6758: 6748: 6738: 6735: 6729: 6726:, let the region 6725: 6720: 6702: 6693: 6684: 6672: 6671: 6659: 6635: 6632: 6630: 6629: 6624: 6616: 6611: 6610: 6598: 6596: 6595: 6592: 6586: 6583: 6582: 6576: 6575: 6549: 6546: 6544: 6542: 6541: 6536: 6534: 6532: 6531: 6528: 6522: 6517: 6516: 6513: 6507: 6502: 6501: 6492: 6472: 6469: 6467: 6466: 6461: 6444: 6442: 6441: 6432: 6427: 6426: 6417: 6412: 6411: 6395: 6393: 6391: 6390: 6385: 6383: 6378: 6370: 6344: 6340: 6338: 6336: 6335: 6330: 6328: 6326: 6325: 6322: 6316: 6295: 6293: 6292: 6287: 6281: 6279: 6278: 6275: 6269: 6268: 6265: 6259: 6244: 6241: 6239: 6237: 6236: 6231: 6229: 6227: 6226: 6217: 6216: 6207: 6204: 6203: 6181: 6177: 6174: 6172: 6170: 6169: 6164: 6162: 6153: 6150: 6149: 6134: 6119: 6095: 6086: 6084: 6083: 6078: 6072: 6067: 6059: 6043: 6039: 6038: 6033: 6029: 6023: 6012: 6003: 6001: 6000: 5995: 5989: 5981: 5961: 5957: 5951: 5945: 5941: 5937: 5935: 5934: 5929: 5927: 5850: 5847: 5843: 5836: 5827: 5821: 5815: 5813: 5812: 5807: 5805: 5797: 5789: 5774: 5759: 5751: 5739: 5717: 5711: 5705: 5699: 5693: 5689: 5688: 5679: 5675: 5668: 5664: 5661: 5654: 5650: 5643: 5637: 5635: 5634: 5629: 5627: 5619: 5611: 5596: 5584: 5576: 5564: 5530: 5521: 5519: 5518: 5513: 5508: 5507: 5506: 5487: 5486: 5485: 5467: 5458: 5445: 5436: 5434: 5433: 5428: 5419: 5394: 5390: 5386: 5384: 5382: 5381: 5376: 5371: 5356: 5352: 5335: 5333: 5332: 5327: 5317: 5303: 5295: 5289: 5277: 5274:) can be written 5267: 5266: 5258: 5245: 5239: 5224: 5221:) is factored as 5203: 5197: 5186: 5179: 5176: 5166: 5146: 5140: 5134: 5124: 5114: 5104: 5094: 5086: 5076: 5070: 5054: 5045: 5043: 5042: 5037: 5032: 5031: 5018: 4996: 4995: 4994: 4976: 4972: 4934: 4930: 4923: 4917: 4913: 4907: 4901: 4897: 4891: 4885: 4879: 4872: 4868: 4862:refractive index 4856: 4843: 4830: 4817: 4804: 4780: 4752: 4743: 4722: 4716: 4710: 4708: 4707: 4702: 4700: 4692: 4677: 4668: 4653: 4633: 4630: 4613: 4568:as a species of 4566:optical rotation 4533:James MacCullagh 4524: 4490: 4481: 4345:coherence length 4329: 4320: 4302: 4300: 4299: 4294: 4289: 4287: 4283: 4282: 4279: 4270: 4269: 4266: 4250: 4246: 4245: 4242: 4233: 4232: 4229: 4213: 4208: 4207: 4204: 4191: 4190: 4177: 4175: 4174: 4169: 4164: 4162: 4158: 4157: 4154: 4145: 4144: 4141: 4125: 4121: 4120: 4117: 4108: 4107: 4104: 4088: 4080: 4079: 4076: 4063: 4062: 4053: 4049: 4046: 4044: 4043: 4035: 4032: 4024: 4022: 4021: 4016: 4014: 4013: 4010: 3998: 3993: 3992: 3989: 3977: 3976: 3964: 3963: 3947: 3946: 3915: 3906: 3893: 3885:evanescent field 3882: 3878: 3867: 3859:in the direction 3856: 3848: 3847: 3845: 3844: 3836: 3833: 3820: 3814: 3812: 3811: 3806: 3804: 3803: 3798: 3789: 3784: 3782: 3781: 3780: 3777: 3765: 3764: 3754: 3753: 3752: 3749: 3737: 3736: 3726: 3695: 3689: 3687: 3686: 3681: 3676: 3675: 3670: 3661: 3643: 3637: 3628: 3613: 3611: 3610: 3602: 3599: 3586: 3567: 3565: 3564: 3559: 3557: 3550: 3548: 3547: 3546: 3543: 3531: 3530: 3518: 3517: 3514: 3502: 3501: 3491: 3490: 3489: 3486: 3474: 3473: 3460: 3451: 3450: 3447: 3434: 3432: 3431: 3430: 3427: 3415: 3414: 3402: 3401: 3398: 3386: 3385: 3375: 3374: 3373: 3370: 3358: 3357: 3345: 3344: 3341: 3329: 3328: 3318: 3309: 3308: 3305: 3292: 3290: 3289: 3288: 3285: 3273: 3272: 3260: 3259: 3256: 3244: 3243: 3233: 3232: 3231: 3228: 3216: 3215: 3202: 3193: 3192: 3189: 3176: 3174: 3173: 3172: 3169: 3157: 3156: 3144: 3143: 3140: 3128: 3127: 3117: 3116: 3115: 3112: 3100: 3099: 3087: 3086: 3083: 3071: 3070: 3060: 3051: 3050: 3047: 3022: 3016: 3015: 3013: 3012: 3007: 3005: 3004: 3003: 2985: 2984: 2982: 2981: 2976: 2974: 2973: 2972: 2959: 2958: 2957: 2939: 2938: 2936: 2935: 2930: 2928: 2927: 2926: 2894: 2872: 2866: 2860: 2846: 2836: 2807: 2798: 2792: 2786: 2747: 2738: 2728: 2719: 2710: 2701: 2692: 2684:Measurements of 2680: 2671: 2660: 2658: 2657: 2652: 2649: 2644: 2641: 2632: 2631: 2628: 2615: 2606: 2597: 2582: 2575: 2569: 2557: 2536: 2506: 2496: 2485:Brewster's angle 2482: 2473: 2464: 2452:Brewster's angle 2446:Brewster's angle 2441: 2431: 2419: 2417: 2416: 2411: 2405: 2404: 2399: 2395: 2393: 2392: 2391: 2379: 2378: 2368: 2367: 2366: 2354: 2353: 2343: 2333: 2332: 2316: 2298:normal incidence 2296:For the case of 2292:Normal incidence 2272: 2270: 2269: 2264: 2259: 2255: 2254: 2253: 2252: 2239: 2238: 2237: 2222: 2214: 2209: 2208: 2207: 2168: 2146: 2140: 2134:) multiplied by 2122: 2120: 2119: 2114: 2112: 2111: 2110: 2091: 2090: 2089: 2072: 2070: 2069: 2064: 2062: 2061: 2060: 2041: 2040: 2039: 2003: 1992: 1990: 1989: 1984: 1978: 1977: 1972: 1968: 1966: 1965: 1964: 1963: 1947: 1946: 1934: 1932: 1931: 1926: 1922: 1921: 1920: 1919: 1903: 1901: 1900: 1891: 1890: 1881: 1867: 1865: 1864: 1854: 1853: 1852: 1851: 1835: 1834: 1822: 1820: 1819: 1814: 1810: 1809: 1808: 1807: 1791: 1789: 1788: 1779: 1778: 1769: 1755: 1753: 1752: 1742: 1732: 1731: 1726: 1722: 1720: 1719: 1718: 1717: 1701: 1700: 1688: 1687: 1686: 1670: 1669: 1659: 1658: 1657: 1656: 1640: 1639: 1627: 1626: 1625: 1609: 1608: 1598: 1588: 1587: 1586: 1570: 1568: 1567: 1562: 1556: 1555: 1550: 1546: 1544: 1543: 1541: 1540: 1535: 1531: 1530: 1529: 1528: 1512: 1510: 1509: 1500: 1499: 1490: 1476: 1474: 1473: 1461: 1460: 1459: 1443: 1442: 1432: 1431: 1429: 1428: 1423: 1419: 1418: 1417: 1416: 1400: 1398: 1397: 1388: 1387: 1378: 1364: 1362: 1361: 1349: 1348: 1347: 1331: 1330: 1320: 1310: 1309: 1304: 1300: 1298: 1297: 1296: 1295: 1279: 1278: 1266: 1265: 1264: 1248: 1247: 1237: 1236: 1235: 1234: 1218: 1217: 1205: 1204: 1203: 1187: 1186: 1176: 1166: 1165: 1164: 1147: 1136: 1127: 1125: 1124: 1119: 1113: 1111: 1110: 1101: 1100: 1091: 1086: 1085: 1069: 1060: 1051: 1019: 1010: 1001: 999: 998: 993: 988: 987: 982: 978: 976: 975: 974: 973: 957: 956: 944: 943: 942: 926: 925: 915: 914: 913: 912: 896: 895: 883: 882: 881: 865: 864: 854: 844: 843: 842: 821: 819: 818: 813: 808: 807: 802: 798: 796: 795: 794: 793: 777: 776: 764: 763: 762: 746: 745: 735: 734: 733: 732: 716: 715: 703: 702: 701: 685: 684: 674: 664: 663: 662: 630: 610: 549:electromagnetism 540: 538: 537: 532: 527: 526: 525: 509: 508: 496: 495: 494: 478: 477: 457: 455: 454: 449: 444: 443: 442: 429: 428: 427: 406: 397: 388: 375: 369: 363: 357: 348: 339: 309: 295: 283: 197: 188: 179:refractive index 152: 151: 148: 147: 144: 141: 138: 135: 132: 129: 66: 57: 21: 17011: 17010: 17006: 17005: 17004: 17002: 17001: 17000: 16986:Physical optics 16961: 16960: 16959: 16947: 16939: 16894: 16861: 16838: 16819: 16800: 16776: 16765: 16759: 16756: 16749: 16742:Further reading 16736: 16732: 16725: 16723:Further reading 16710:E. T. Whittaker 16701: 16688: 16626: 16616: 16566: 16561: 16560: 16555: 16551: 16544: 16540: 16536: 16526: 16522: 16507:10.1063/1.93043 16483: 16479: 16474: 16470: 16463: 16451: 16447: 16441: 16437: 16430: 16426: 16422: 16418: 16416: 16412: 16405: 16403: 16399: 16384: 16380: 16377: 16373: 16366: 16364: 16360: 16353: 16349: 16347: 16343: 16336: 16332: 16328: 16324: 16322: 16318: 16313: 16309: 16302: 16298: 16296: 16292: 16285: 16281: 16277: 16274: 16267: 16242: 16238: 16234: 16230: 16224: 16220: 16213: 16209: 16207: 16203: 16192: 16188: 16180: 16178: 16174: 16167: 16163: 16153: 16149: 16142: 16140: 16136: 16124: 16120: 16113: 16111: 16107: 16102: 16098: 16093: 16089: 16084: 16080: 16075: 16071: 16066: 16062: 16057: 16053: 16048: 16044: 16039: 16035: 16030: 16026: 16019: 16017: 16013: 16006: 16004: 15997: 15987:Wayback Machine 15977: 15970: 15965: 15961: 15954: 15932: 15928: 15923: 15919: 15914: 15910: 15905: 15900: 15899: 15890: 15883: 15873: 15870: 15868: 15864: 15855: 15849: 15845: 15835: 15829: 15820: 15815: 15803: 15799: 15794: 15756:Reflection loss 15726: 15689:§ History 15679: 15674: 15672: 15666: 15663: 15659: 15654: 15653: 15647: 15644: 15635: 15629: 15626: 15620: 15605: 15599: 15593: 15577: 15569: 15563: 15557: 15541: 15500: 15496: 15491: 15485: 15481: 15463: 15459: 15457: 15454: 15453: 15444: 15442: 15434: 15432: 15429: 15425: 15423: 15415: 15413: 15410: 15402: 15397: 15396: 15390: 15387: 15383: 15378: 15377: 15369: 15365: 15364: 15355: 15354: 15346: 15342: 15341: 15335: 15332: 15321: 15320: 15312: 15310: 15307: 15303: 15301: 15293: 15291: 15288: 15283: 15282: 15274: 15272: 15269: 15265: 15263: 15255: 15253: 15250: 15241: 15235: 15232: 15226: 15223: 15208: 15171: 15158: 15154: 15142: 15138: 15129: 15125: 15113: 15109: 15108: 15101: 15097: 15085: 15081: 15072: 15068: 15056: 15052: 15051: 15049: 15045: 15044: 15035: 15031: 15029: 15026: 15025: 14990: 14977: 14973: 14961: 14957: 14948: 14944: 14932: 14928: 14927: 14920: 14916: 14904: 14900: 14891: 14887: 14875: 14871: 14870: 14868: 14864: 14863: 14854: 14850: 14848: 14845: 14844: 14799: 14795: 14786: 14782: 14781: 14774: 14770: 14766: 14764: 14755: 14751: 14749: 14746: 14745: 14707: 14703: 14694: 14690: 14689: 14682: 14678: 14669: 14665: 14664: 14662: 14653: 14649: 14647: 14644: 14643: 14605: 14601: 14592: 14588: 14587: 14580: 14576: 14572: 14570: 14561: 14557: 14555: 14552: 14551: 14513: 14509: 14500: 14496: 14495: 14488: 14484: 14475: 14471: 14470: 14468: 14459: 14455: 14453: 14450: 14449: 14404: 14400: 14388: 14384: 14375: 14371: 14359: 14355: 14354: 14347: 14343: 14331: 14327: 14323: 14321: 14312: 14308: 14306: 14303: 14302: 14264: 14260: 14248: 14244: 14235: 14231: 14219: 14215: 14214: 14207: 14203: 14191: 14187: 14178: 14174: 14162: 14158: 14157: 14155: 14146: 14142: 14140: 14137: 14136: 14097: 14093: 14081: 14077: 14068: 14064: 14052: 14048: 14047: 14040: 14036: 14024: 14020: 14016: 14014: 14005: 14001: 13999: 13996: 13995: 13957: 13953: 13941: 13937: 13928: 13924: 13912: 13908: 13907: 13900: 13896: 13884: 13880: 13871: 13867: 13855: 13851: 13850: 13848: 13839: 13835: 13833: 13830: 13829: 13822: 13769: 13765: 13760: 13754: 13750: 13748: 13739: 13735: 13708: 13704: 13699: 13693: 13689: 13687: 13678: 13674: 13672: 13669: 13668: 13662: 13659: 13653: 13623: 13618: 13610: 13607: 13606: 13591: 13542: 13540: 13531: 13530: 13524: 13521: 13506: 13473: 13470: 13469: 13449: 13445: 13436: 13432: 13419: 13411: 13408: 13407: 13388: 13384: 13375: 13371: 13358: 13350: 13347: 13346: 13336: 13301: 13290: 13286: 13274: 13270: 13261: 13257: 13245: 13241: 13240: 13236: 13235: 13228: 13224: 13212: 13208: 13196: 13192: 13186: 13182: 13178: 13176: 13164: 13160: 13153: 13146: 13142: 13135: 13133: 13124: 13120: 13112: 13108: 13106: 13104: 13098: 13085: 13081: 13069: 13065: 13056: 13052: 13040: 13036: 13035: 13028: 13024: 13012: 13008: 13004: 13002: 12998: 12997: 12988: 12984: 12982: 12979: 12978: 12938: 12927: 12923: 12911: 12907: 12898: 12894: 12882: 12878: 12877: 12873: 12872: 12865: 12861: 12849: 12845: 12833: 12829: 12823: 12819: 12815: 12813: 12801: 12797: 12790: 12783: 12779: 12772: 12770: 12761: 12757: 12749: 12745: 12743: 12741: 12735: 12722: 12718: 12706: 12702: 12693: 12689: 12677: 12673: 12672: 12665: 12661: 12649: 12645: 12641: 12639: 12635: 12634: 12625: 12621: 12619: 12616: 12615: 12606: 12601: 12596: 12592: 12538: 12527: 12523: 12511: 12507: 12498: 12494: 12482: 12478: 12477: 12473: 12472: 12462: 12458: 12446: 12442: 12430: 12426: 12420: 12416: 12408: 12403: 12401: 12391: 12387: 12372: 12368: 12366: 12363: 12362: 12322: 12311: 12307: 12295: 12291: 12282: 12278: 12266: 12262: 12261: 12257: 12256: 12246: 12242: 12230: 12226: 12214: 12210: 12204: 12200: 12192: 12187: 12185: 12175: 12171: 12156: 12152: 12150: 12147: 12146: 12137: 12131: +  12127: 12123: 12099: 12095: 12062: 12049: 12045: 12033: 12029: 12020: 12016: 12004: 12000: 11999: 11992: 11988: 11976: 11972: 11963: 11959: 11947: 11943: 11942: 11940: 11936: 11935: 11926: 11922: 11920: 11917: 11916: 11878: 11865: 11861: 11849: 11845: 11836: 11832: 11820: 11816: 11815: 11808: 11804: 11792: 11788: 11779: 11775: 11763: 11759: 11758: 11756: 11752: 11751: 11742: 11738: 11736: 11733: 11732: 11697: 11686: 11685: 11678: 11672: 11666: 11662: 11658: 11648: 11644: 11635: 11632: 11628: 11621: 11615: 11605: 11599: 11595: 11591: 11585: 11579: 11575: 11571: 11565: 11559: 11553: 11543: 11537: 11528: 11524: 11517: 11511: 11508: 11505: 11504: 11502: 11501: 11498: 11488:Poynting vector 11483: 11438: 11432: 11429: 11425: 11422: 11416: 11413: 11408: 11406: 11398: 11396: 11393: 11392:, we again have 11387: 11386: 11379: 11374: 11334: 11330: 11321: 11317: 11316: 11309: 11305: 11301: 11299: 11290: 11286: 11284: 11281: 11280: 11239: 11235: 11226: 11222: 11221: 11214: 11210: 11201: 11197: 11196: 11194: 11185: 11181: 11179: 11176: 11175: 11162: 11161: 11155: 11154: 11148: 11145: 11102: 11098: 11086: 11082: 11073: 11069: 11057: 11053: 11052: 11045: 11041: 11029: 11025: 11021: 11019: 11010: 11006: 11004: 11001: 11000: 10959: 10955: 10943: 10939: 10930: 10926: 10914: 10910: 10909: 10902: 10898: 10886: 10882: 10873: 10869: 10857: 10853: 10852: 10850: 10841: 10837: 10835: 10832: 10831: 10821: 10820: 10814: 10811: 10805: 10775: 10774: 10764: 10760: 10754: 10750: 10742: 10736: 10732: 10726: 10722: 10713: 10709: 10706: 10705: 10699: 10695: 10683: 10679: 10671: 10665: 10661: 10649: 10645: 10636: 10632: 10622: 10620: 10617: 10616: 10542: 10519: 10518: 10512: 10508: 10501: 10495: 10491: 10482: 10478: 10475: 10474: 10468: 10464: 10452: 10448: 10441: 10435: 10431: 10419: 10415: 10406: 10402: 10390: 10386: 10382: 10381: 10378: 10376: 10373: 10372: 10361: 10355: 10325: 10324: 10311: 10305: 10300: 10299: 10295: 10291: 10284: 10280: 10274: 10270: 10262: 10256: 10252: 10249: 10248: 10238: 10232: 10227: 10226: 10222: 10218: 10211: 10207: 10201: 10197: 10189: 10183: 10179: 10176: 10175: 10165: 10159: 10154: 10153: 10149: 10145: 10139: 10135: 10127: 10121: 10117: 10113: 10111: 10108: 10107: 10097: 10092: 10088: 10085: 10082: 10078: 10070: 10066: 10065: 10057: 10055: 10049: 10046: 10040: 10034: 10022: 10012: 10008: 10002: 9996: 9992: 9985: 9978: 9973: 9970: 9964: 9934: 9933: 9920: 9914: 9909: 9908: 9904: 9900: 9893: 9889: 9882: 9876: 9872: 9869: 9868: 9858: 9852: 9847: 9846: 9842: 9838: 9831: 9827: 9820: 9814: 9810: 9807: 9806: 9796: 9790: 9785: 9784: 9780: 9776: 9769: 9763: 9759: 9755: 9753: 9750: 9749: 9738: 9735: 9729: 9726: 9720: 9716: 9708: 9704: 9703: 9695: 9693: 9687: 9684: 9678: 9671: 9656: 9655: 9649: 9646: 9642: 9637: 9633: 9632: 9626: 9623: 9618: 9614: 9613: 9605: 9603: 9600: 9594: 9593: 9586: 9583: 9540: 9536: 9527: 9523: 9522: 9515: 9511: 9507: 9505: 9496: 9492: 9490: 9487: 9486: 9445: 9441: 9432: 9428: 9427: 9420: 9416: 9407: 9403: 9402: 9400: 9391: 9387: 9385: 9382: 9381: 9368: 9367: 9361: 9360: 9354: 9351: 9308: 9304: 9292: 9288: 9279: 9275: 9263: 9259: 9258: 9251: 9247: 9235: 9231: 9227: 9225: 9216: 9212: 9210: 9207: 9206: 9165: 9161: 9149: 9145: 9136: 9132: 9120: 9116: 9115: 9108: 9104: 9092: 9088: 9079: 9075: 9063: 9059: 9058: 9056: 9047: 9043: 9041: 9038: 9037: 9027: 9026: 9020: 9017: 9011: 8981: 8980: 8970: 8966: 8954: 8950: 8944: 8940: 8932: 8926: 8922: 8910: 8906: 8900: 8896: 8887: 8883: 8871: 8867: 8864: 8863: 8857: 8853: 8845: 8839: 8835: 8825: 8823: 8820: 8819: 8745: 8722: 8721: 8715: 8711: 8699: 8695: 8688: 8682: 8678: 8666: 8662: 8653: 8649: 8637: 8633: 8630: 8629: 8623: 8619: 8612: 8606: 8602: 8593: 8589: 8585: 8584: 8581: 8579: 8576: 8575: 8564: 8558: 8524: 8523: 8510: 8504: 8499: 8498: 8494: 8490: 8483: 8479: 8473: 8469: 8461: 8455: 8451: 8448: 8447: 8437: 8431: 8426: 8425: 8421: 8417: 8410: 8406: 8400: 8396: 8388: 8382: 8378: 8375: 8374: 8364: 8358: 8353: 8352: 8348: 8344: 8338: 8334: 8326: 8320: 8316: 8312: 8310: 8307: 8306: 8296: 8288: 8285: 8281: 8273: 8269: 8268: 8260: 8258: 8252: 8249: 8243: 8239: 8232: 8225: 8220: 8217: 8211: 8205: 8199: 8193: 8155: 8154: 8141: 8135: 8130: 8129: 8125: 8121: 8114: 8110: 8103: 8097: 8093: 8090: 8089: 8079: 8073: 8068: 8067: 8063: 8059: 8052: 8048: 8041: 8035: 8031: 8027: 8025: 8022: 8021: 7976: 7970: 7965: 7964: 7960: 7956: 7947: 7943: 7941: 7938: 7937: 7926: 7914: 7910: 7904: 7901: 7895: 7889: 7883: 7877: 7870: 7827: 7823: 7805: 7801: 7790: 7784: 7779: 7778: 7767: 7761: 7756: 7755: 7744: 7738: 7733: 7732: 7708: 7705: 7704: 7668: 7667: 7654: 7650: 7635: 7631: 7622: 7618: 7603: 7599: 7586: 7578: 7572: 7567: 7566: 7563: 7562: 7553: 7549: 7531: 7527: 7506: 7502: 7495: 7487: 7481: 7476: 7475: 7472: 7471: 7462: 7458: 7440: 7436: 7415: 7411: 7404: 7396: 7390: 7385: 7384: 7380: 7378: 7375: 7374: 7345: 7344: 7331: 7327: 7315: 7311: 7305: 7296: 7292: 7280: 7276: 7270: 7255: 7254: 7245: 7241: 7230: 7221: 7217: 7206: 7194: 7190: 7183: 7177: 7172: 7171: 7168: 7167: 7158: 7154: 7143: 7134: 7130: 7119: 7107: 7103: 7096: 7090: 7085: 7084: 7081: 7080: 7071: 7067: 7056: 7047: 7043: 7032: 7020: 7016: 7009: 7003: 6998: 6997: 6993: 6991: 6988: 6987: 6981: 6975: 6971: 6965: 6962: 6956: 6950: 6944: 6940: 6936: 6928: 6919: 6889: 6879: 6874: 6873: 6867: 6861: 6855: 6852: 6846: 6840: 6834: 6828: 6818: 6812: 6806: 6800: 6796: 6790: 6786: 6780: 6776: 6771: 6767: 6763: 6760: 6756: 6750: 6746: 6740: 6736: 6730: 6727: 6718: 6708: 6701: 6695: 6692: 6686: 6682: 6674: 6669: 6668: 6657: 6656: 6648: 6641: 6633: 6612: 6606: 6602: 6591: 6587: 6585: 6578: 6577: 6571: 6567: 6559: 6556: 6555: 6547: 6527: 6523: 6518: 6512: 6508: 6506: 6497: 6493: 6488: 6483: 6480: 6479: 6478: 6477:. By division, 6470: 6437: 6433: 6428: 6422: 6418: 6416: 6407: 6403: 6401: 6398: 6397: 6374: 6369: 6361: 6358: 6357: 6356: 6342: 6321: 6317: 6315: 6307: 6304: 6303: 6301: 6274: 6270: 6264: 6260: 6258: 6250: 6247: 6246: 6242: 6222: 6218: 6212: 6208: 6206: 6199: 6198: 6187: 6184: 6183: 6182: 6179: 6175: 6152: 6145: 6144: 6130: 6125: 6122: 6121: 6120: 6117: 6063: 6058: 6050: 6047: 6046: 6036: 6031: 6027: 6024: 6021: 5980: 5968: 5965: 5964: 5953: 5947: 5943: 5939: 5925: 5924: 5907: 5895: 5894: 5881: 5868: 5866: 5863: 5862: 5848: 5841: 5834: 5829: 5823: 5817: 5803: 5802: 5793: 5785: 5775: 5770: 5761: 5760: 5755: 5747: 5740: 5735: 5725: 5723: 5720: 5719: 5713: 5707: 5701: 5695: 5691: 5686: 5677: 5673: 5669: 5666: 5662: 5652: 5648: 5644: 5641: 5625: 5624: 5615: 5607: 5597: 5592: 5586: 5585: 5580: 5572: 5565: 5560: 5553: 5551: 5548: 5547: 5496: 5492: 5488: 5481: 5477: 5476: 5474: 5471: 5470: 5454: 5415: 5401: 5398: 5397: 5388: 5367: 5362: 5359: 5358: 5357: 5354: 5350: 5343: 5313: 5308: 5305: 5304: 5301: 5291: 5283: 5278: 5275: 5264: 5260: 5254: 5241: 5230: 5225: 5222: 5199: 5188: 5181: 5177: 5168: 5162: 5153:To advance the 5142: 5136: 5130: 5120: 5110: 5107:position vector 5100: 5095:is the angular 5092: 5082: 5072: 5068: 5063: 5008: 5001: 4997: 4990: 4986: 4985: 4983: 4980: 4979: 4968: 4958: 4938:In the case of 4932: 4928: 4919: 4915: 4909: 4903: 4899: 4893: 4887: 4881: 4877: 4870: 4864: 4855: 4845: 4842: 4836: 4829: 4823: 4815: 4809: 4803: 4792: 4786: 4779: 4768: 4762: 4751: 4745: 4742: 4736: 4718: 4712: 4698: 4697: 4688: 4678: 4673: 4670: 4669: 4664: 4654: 4649: 4645: 4643: 4640: 4639: 4631: 4614: 4611: 4596: 4588: 4522: 4489: 4483: 4480: 4474: 4468:Hendrik Lorentz 4464:electromagnetic 4393: 4387: 4372:optical filters 4336: 4327: 4321: 4318: 4278: 4274: 4265: 4261: 4251: 4241: 4237: 4228: 4224: 4214: 4212: 4203: 4199: 4197: 4194: 4193: 4188: 4187: 4181: 4153: 4149: 4140: 4136: 4126: 4116: 4112: 4103: 4099: 4089: 4087: 4075: 4071: 4069: 4066: 4065: 4060: 4059: 4051: 4047: 4042: 4036: 4033: 4030: 4029: 4027: 4026: 4009: 4005: 3994: 3988: 3984: 3972: 3968: 3959: 3955: 3953: 3950: 3949: 3944: 3943: 3937: 3934: 3914: 3908: 3905: 3899: 3888: 3880: 3876: 3871:In the case of 3862: 3850: 3843: 3837: 3834: 3832: 3826: 3825: 3823: 3822: 3816: 3799: 3794: 3793: 3785: 3776: 3772: 3760: 3756: 3755: 3748: 3744: 3732: 3728: 3727: 3725: 3717: 3714: 3713: 3693: 3671: 3666: 3665: 3657: 3649: 3646: 3645: 3639: 3633: 3626: 3619: 3609: 3603: 3600: 3598: 3592: 3591: 3589: 3588: 3584: 3577: 3571: 3555: 3554: 3542: 3538: 3526: 3522: 3513: 3509: 3497: 3493: 3492: 3485: 3481: 3469: 3465: 3461: 3459: 3452: 3446: 3442: 3439: 3438: 3426: 3422: 3410: 3406: 3397: 3393: 3381: 3377: 3376: 3369: 3365: 3353: 3349: 3340: 3336: 3324: 3320: 3319: 3317: 3310: 3304: 3300: 3297: 3296: 3284: 3280: 3268: 3264: 3255: 3251: 3239: 3235: 3234: 3227: 3223: 3211: 3207: 3203: 3201: 3194: 3188: 3184: 3181: 3180: 3168: 3164: 3152: 3148: 3139: 3135: 3123: 3119: 3118: 3111: 3107: 3095: 3091: 3082: 3078: 3066: 3062: 3061: 3059: 3052: 3046: 3042: 3038: 3036: 3033: 3032: 3018: 2999: 2998: 2994: 2992: 2989: 2988: 2987: 2968: 2967: 2963: 2953: 2952: 2948: 2946: 2943: 2942: 2941: 2922: 2921: 2917: 2915: 2912: 2911: 2910: 2890: 2868: 2862: 2856: 2842: 2832: 2806: 2800: 2794: 2788: 2782: 2755: 2746: 2740: 2737: 2731: 2727: 2721: 2718: 2712: 2709: 2703: 2700: 2694: 2691: 2685: 2679: 2673: 2670: 2664: 2645: 2640: 2627: 2623: 2621: 2618: 2617: 2614: 2608: 2605: 2599: 2592: 2589: 2577: 2571: 2563: 2555: 2548: 2542: 2535: 2528: 2522: 2519: 2513: 2504: 2498: 2494: 2488: 2481: 2475: 2472: 2466: 2463: 2457: 2454: 2448: 2439: 2433: 2429: 2423: 2400: 2387: 2383: 2374: 2370: 2369: 2362: 2358: 2349: 2345: 2344: 2342: 2338: 2337: 2328: 2324: 2322: 2319: 2318: 2314: 2307: 2301: 2294: 2289: 2283:is often used. 2248: 2247: 2243: 2233: 2232: 2228: 2227: 2223: 2213: 2197: 2196: 2192: 2190: 2187: 2186: 2166: 2159: 2152: 2142: 2135: 2132:Poynting vector 2106: 2105: 2101: 2085: 2084: 2080: 2078: 2075: 2074: 2056: 2055: 2051: 2035: 2034: 2030: 2028: 2025: 2024: 2002: 1996: 1973: 1959: 1958: 1954: 1942: 1938: 1927: 1915: 1914: 1910: 1896: 1892: 1886: 1882: 1880: 1879: 1875: 1874: 1866: 1860: 1856: 1855: 1847: 1846: 1842: 1830: 1826: 1815: 1803: 1802: 1798: 1784: 1780: 1774: 1770: 1768: 1767: 1763: 1762: 1754: 1748: 1744: 1743: 1741: 1737: 1736: 1727: 1713: 1712: 1708: 1696: 1692: 1682: 1681: 1677: 1665: 1661: 1660: 1652: 1651: 1647: 1635: 1631: 1621: 1620: 1616: 1604: 1600: 1599: 1597: 1593: 1592: 1582: 1581: 1577: 1575: 1572: 1571: 1551: 1536: 1524: 1523: 1519: 1505: 1501: 1495: 1491: 1489: 1488: 1484: 1483: 1475: 1469: 1465: 1455: 1454: 1450: 1438: 1434: 1433: 1424: 1412: 1411: 1407: 1393: 1389: 1383: 1379: 1377: 1376: 1372: 1371: 1363: 1357: 1353: 1343: 1342: 1338: 1326: 1322: 1321: 1319: 1315: 1314: 1305: 1291: 1290: 1286: 1274: 1270: 1260: 1259: 1255: 1243: 1239: 1238: 1230: 1229: 1225: 1213: 1209: 1199: 1198: 1194: 1182: 1178: 1177: 1175: 1171: 1170: 1160: 1159: 1155: 1153: 1150: 1149: 1142: 1135: 1129: 1106: 1102: 1096: 1092: 1090: 1081: 1077: 1075: 1072: 1071: 1068: 1062: 1059: 1053: 1049: 1041: 1034: 1028: 1022:wave impedances 1018: 1012: 1009: 1003: 983: 969: 968: 964: 952: 948: 938: 937: 933: 921: 917: 916: 908: 907: 903: 891: 887: 877: 876: 872: 860: 856: 855: 853: 849: 848: 838: 837: 833: 831: 828: 827: 803: 789: 788: 784: 772: 768: 758: 757: 753: 741: 737: 736: 728: 727: 723: 711: 707: 697: 696: 692: 680: 676: 675: 673: 669: 668: 658: 657: 653: 651: 648: 647: 626: 606: 569: 521: 520: 516: 504: 500: 490: 489: 485: 473: 469: 467: 464: 463: 438: 437: 433: 423: 422: 418: 416: 413: 412: 405: 399: 396: 390: 387: 381: 371: 365: 359: 356: 350: 347: 341: 335: 320: 304: 293: 281: 245: 239: 196: 190: 187: 181: 175: 155:transverse wave 126: 122: 92: 91: 90: 89: 69: 68: 67: 59: 58: 39: 28: 23: 22: 15: 12: 11: 5: 17009: 16999: 16998: 16993: 16988: 16983: 16978: 16973: 16958: 16957: 16937: 16936: 16930: 16924: 16918: 16912: 16906: 16901: 16893: 16892:External links 16890: 16889: 16888: 16875: 16865: 16859: 16842: 16836: 16823: 16817: 16804: 16798: 16778: 16777: 16739: 16737: 16730: 16724: 16721: 16720: 16719: 16707: 16692: 16677: 16662: 16647: 16632: 16613: 16598: 16591: 16576: 16565: 16562: 16559: 16558: 16549: 16520: 16493:(3): 210–212. 16477: 16468: 16435: 16410: 16397: 16371: 16358: 16341: 16316: 16307: 16290: 16265: 16218: 16201: 16172: 16147: 16134: 16118: 16105: 16096: 16087: 16078: 16069: 16060: 16051: 16042: 16033: 16024: 16011: 15995: 15968: 15959: 15952: 15926: 15917: 15907: 15906: 15904: 15901: 15898: 15897: 15862: 15818: 15796: 15795: 15793: 15790: 15789: 15788: 15783: 15778: 15773: 15771:Snell's window 15768: 15763: 15758: 15753: 15747: 15742: 15737: 15732: 15730:Jones calculus 15725: 15722: 15670: 15651: 15633: 15624: 15607:). Hence, in ( 15603: 15597: 15540: 15537: 15531: 15530: 15521: 15519: 15508: 15503: 15499: 15494: 15488: 15484: 15480: 15477: 15474: 15471: 15462: 15440: 15421: 15409:. Substituting 15407:Brewster angle 15394: 15375: 15362: 15352: 15339: 15318: 15299: 15280: 15261: 15239: 15230: 15222: 15219: 15203: 15202: 15193: 15191: 15180: 15174: 15169: 15157: 15153: 15150: 15145: 15141: 15137: 15128: 15124: 15121: 15116: 15112: 15100: 15096: 15093: 15088: 15084: 15080: 15071: 15067: 15064: 15059: 15055: 15048: 15043: 15034: 15018: 15017: 15008: 15006: 14993: 14988: 14976: 14972: 14969: 14964: 14960: 14956: 14947: 14943: 14940: 14935: 14931: 14919: 14915: 14912: 14907: 14903: 14899: 14890: 14886: 14883: 14878: 14874: 14867: 14862: 14853: 14834: 14833: 14824: 14822: 14811: 14802: 14798: 14794: 14789: 14785: 14777: 14773: 14769: 14763: 14754: 14738: 14737: 14728: 14726: 14710: 14706: 14702: 14697: 14693: 14685: 14681: 14677: 14672: 14668: 14661: 14652: 14636: 14635: 14626: 14624: 14608: 14604: 14600: 14595: 14591: 14583: 14579: 14575: 14569: 14560: 14544: 14543: 14534: 14532: 14516: 14512: 14508: 14503: 14499: 14491: 14487: 14483: 14478: 14474: 14467: 14458: 14439: 14438: 14429: 14427: 14416: 14403: 14399: 14396: 14391: 14387: 14383: 14374: 14370: 14367: 14362: 14358: 14346: 14342: 14339: 14334: 14330: 14326: 14320: 14311: 14295: 14294: 14285: 14283: 14263: 14259: 14256: 14251: 14247: 14243: 14234: 14230: 14227: 14222: 14218: 14206: 14202: 14199: 14194: 14190: 14186: 14177: 14173: 14170: 14165: 14161: 14154: 14145: 14129: 14128: 14119: 14117: 14096: 14092: 14089: 14084: 14080: 14076: 14067: 14063: 14060: 14055: 14051: 14039: 14035: 14032: 14027: 14023: 14019: 14013: 14004: 13988: 13987: 13978: 13976: 13956: 13952: 13949: 13944: 13940: 13936: 13927: 13923: 13920: 13915: 13911: 13899: 13895: 13892: 13887: 13883: 13879: 13870: 13866: 13863: 13858: 13854: 13847: 13838: 13820: 13816:), the factor 13781: 13772: 13768: 13764: 13757: 13753: 13747: 13742: 13738: 13725: 13711: 13707: 13703: 13696: 13692: 13686: 13681: 13677: 13657: 13638: 13630: 13627: 13622: 13617: 13614: 13590: 13587: 13583:Mie scattering 13538: 13528: 13505: 13502: 13489: 13486: 13483: 13480: 13477: 13457: 13452: 13448: 13444: 13439: 13435: 13431: 13426: 13423: 13418: 13415: 13396: 13391: 13387: 13383: 13378: 13374: 13370: 13365: 13362: 13357: 13354: 13331: 13330: 13321: 13319: 13304: 13299: 13289: 13285: 13282: 13277: 13273: 13269: 13260: 13256: 13253: 13248: 13244: 13239: 13227: 13223: 13220: 13211: 13207: 13204: 13199: 13195: 13189: 13185: 13181: 13175: 13163: 13159: 13156: 13145: 13141: 13138: 13127: 13123: 13115: 13111: 13101: 13096: 13084: 13080: 13077: 13072: 13068: 13064: 13055: 13051: 13048: 13043: 13039: 13027: 13023: 13020: 13015: 13011: 13007: 13001: 12996: 12987: 12968: 12967: 12958: 12956: 12941: 12936: 12926: 12922: 12919: 12914: 12910: 12906: 12897: 12893: 12890: 12885: 12881: 12876: 12864: 12860: 12857: 12848: 12844: 12841: 12836: 12832: 12826: 12822: 12818: 12812: 12800: 12796: 12793: 12782: 12778: 12775: 12764: 12760: 12752: 12748: 12738: 12733: 12721: 12717: 12714: 12709: 12705: 12701: 12692: 12688: 12685: 12680: 12676: 12664: 12660: 12657: 12652: 12648: 12644: 12638: 12633: 12624: 12568: 12567: 12558: 12556: 12541: 12536: 12526: 12522: 12519: 12514: 12510: 12506: 12497: 12493: 12490: 12485: 12481: 12476: 12470: 12461: 12457: 12454: 12445: 12441: 12438: 12433: 12429: 12423: 12419: 12415: 12406: 12399: 12390: 12386: 12383: 12380: 12371: 12352: 12351: 12342: 12340: 12325: 12320: 12310: 12306: 12303: 12298: 12294: 12290: 12281: 12277: 12274: 12269: 12265: 12260: 12254: 12245: 12241: 12238: 12229: 12225: 12222: 12217: 12213: 12207: 12203: 12199: 12190: 12183: 12174: 12170: 12167: 12164: 12155: 12115:transmissivity 12090: 12089: 12080: 12078: 12065: 12060: 12048: 12044: 12041: 12036: 12032: 12028: 12019: 12015: 12012: 12007: 12003: 11991: 11987: 11984: 11979: 11975: 11971: 11962: 11958: 11955: 11950: 11946: 11939: 11934: 11925: 11906: 11905: 11896: 11894: 11881: 11876: 11864: 11860: 11857: 11852: 11848: 11844: 11835: 11831: 11828: 11823: 11819: 11807: 11803: 11800: 11795: 11791: 11787: 11778: 11774: 11771: 11766: 11762: 11755: 11750: 11741: 11665:component) of 11598:components of 11578:components of 11482: 11479: 11436: 11420: 11404: 11384: 11369: 11368: 11359: 11357: 11346: 11337: 11333: 11329: 11324: 11320: 11312: 11308: 11304: 11298: 11289: 11270: 11269: 11260: 11258: 11242: 11238: 11234: 11229: 11225: 11217: 11213: 11209: 11204: 11200: 11193: 11184: 11159: 11152: 11137: 11136: 11127: 11125: 11114: 11101: 11097: 11094: 11089: 11085: 11081: 11072: 11068: 11065: 11060: 11056: 11044: 11040: 11037: 11032: 11028: 11024: 11018: 11009: 10990: 10989: 10980: 10978: 10958: 10954: 10951: 10946: 10942: 10938: 10929: 10925: 10922: 10917: 10913: 10901: 10897: 10894: 10889: 10885: 10881: 10872: 10868: 10865: 10860: 10856: 10849: 10840: 10818: 10809: 10800: 10799: 10790: 10788: 10773: 10763: 10757: 10753: 10748: 10745: 10743: 10735: 10729: 10725: 10721: 10716: 10712: 10708: 10707: 10698: 10694: 10691: 10682: 10677: 10674: 10672: 10664: 10660: 10657: 10648: 10644: 10635: 10631: 10628: 10625: 10624: 10588: 10587: 10578: 10576: 10565: 10561: 10558: 10555: 10531: 10511: 10507: 10504: 10502: 10494: 10490: 10481: 10477: 10476: 10467: 10463: 10460: 10451: 10447: 10444: 10442: 10434: 10430: 10427: 10418: 10414: 10405: 10401: 10398: 10389: 10385: 10384: 10380: 10350: 10349: 10340: 10338: 10323: 10317: 10314: 10303: 10298: 10294: 10287: 10283: 10277: 10273: 10268: 10265: 10263: 10255: 10251: 10250: 10244: 10241: 10230: 10225: 10221: 10214: 10210: 10204: 10200: 10195: 10192: 10190: 10182: 10178: 10177: 10171: 10168: 10157: 10152: 10148: 10142: 10138: 10133: 10130: 10128: 10120: 10116: 10115: 10076: 10063: 10053: 9959: 9958: 9949: 9947: 9932: 9926: 9923: 9912: 9907: 9903: 9896: 9892: 9888: 9885: 9883: 9875: 9871: 9870: 9864: 9861: 9850: 9845: 9841: 9834: 9830: 9826: 9823: 9821: 9813: 9809: 9808: 9802: 9799: 9788: 9783: 9779: 9775: 9772: 9770: 9762: 9758: 9757: 9733: 9724: 9714: 9701: 9691: 9670: 9663: 9653: 9630: 9611: 9591: 9575: 9574: 9565: 9563: 9552: 9543: 9539: 9535: 9530: 9526: 9518: 9514: 9510: 9504: 9495: 9476: 9475: 9466: 9464: 9448: 9444: 9440: 9435: 9431: 9423: 9419: 9415: 9410: 9406: 9399: 9390: 9365: 9358: 9343: 9342: 9333: 9331: 9320: 9307: 9303: 9300: 9295: 9291: 9287: 9278: 9274: 9271: 9266: 9262: 9250: 9246: 9243: 9238: 9234: 9230: 9224: 9215: 9196: 9195: 9186: 9184: 9164: 9160: 9157: 9152: 9148: 9144: 9135: 9131: 9128: 9123: 9119: 9107: 9103: 9100: 9095: 9091: 9087: 9078: 9074: 9071: 9066: 9062: 9055: 9046: 9024: 9015: 9006: 9005: 8996: 8994: 8979: 8969: 8965: 8962: 8953: 8947: 8943: 8938: 8935: 8933: 8925: 8921: 8918: 8909: 8903: 8899: 8895: 8886: 8882: 8879: 8874: 8870: 8866: 8865: 8856: 8851: 8848: 8846: 8838: 8834: 8831: 8828: 8827: 8791: 8790: 8781: 8779: 8768: 8764: 8761: 8758: 8734: 8714: 8710: 8707: 8698: 8694: 8691: 8689: 8681: 8677: 8674: 8665: 8661: 8652: 8648: 8645: 8636: 8632: 8631: 8622: 8618: 8615: 8613: 8605: 8601: 8592: 8588: 8587: 8583: 8549: 8548: 8539: 8537: 8522: 8516: 8513: 8502: 8497: 8493: 8486: 8482: 8476: 8472: 8467: 8464: 8462: 8454: 8450: 8449: 8443: 8440: 8429: 8424: 8420: 8413: 8409: 8403: 8399: 8394: 8391: 8389: 8381: 8377: 8376: 8370: 8367: 8356: 8351: 8347: 8341: 8337: 8332: 8329: 8327: 8319: 8315: 8314: 8279: 8266: 8256: 8180: 8179: 8170: 8168: 8153: 8147: 8144: 8133: 8128: 8124: 8117: 8113: 8109: 8106: 8104: 8096: 8092: 8091: 8085: 8082: 8071: 8066: 8062: 8055: 8051: 8047: 8044: 8042: 8034: 8030: 8029: 8011: 8010: 8001: 7999: 7988: 7982: 7979: 7968: 7963: 7959: 7955: 7946: 7931:-component is 7908: 7899: 7869: 7862: 7859: 7858: 7849: 7847: 7836: 7826: 7822: 7819: 7816: 7813: 7808: 7804: 7800: 7796: 7793: 7782: 7777: 7773: 7770: 7759: 7754: 7750: 7747: 7736: 7722: 7718: 7715: 7712: 7693: 7692: 7683: 7681: 7666: 7662: 7653: 7649: 7646: 7643: 7638: 7634: 7630: 7621: 7617: 7614: 7611: 7606: 7602: 7598: 7595: 7592: 7589: 7587: 7584: 7581: 7570: 7565: 7564: 7561: 7552: 7548: 7545: 7542: 7539: 7530: 7526: 7523: 7520: 7517: 7514: 7509: 7505: 7501: 7498: 7496: 7493: 7490: 7479: 7474: 7473: 7470: 7461: 7457: 7454: 7451: 7448: 7439: 7435: 7432: 7429: 7426: 7423: 7418: 7414: 7410: 7407: 7405: 7402: 7399: 7388: 7383: 7382: 7343: 7339: 7330: 7326: 7323: 7318: 7314: 7308: 7304: 7295: 7291: 7288: 7283: 7279: 7273: 7269: 7266: 7263: 7260: 7258: 7256: 7253: 7244: 7240: 7237: 7233: 7229: 7220: 7216: 7213: 7209: 7205: 7202: 7197: 7193: 7189: 7186: 7184: 7175: 7170: 7169: 7166: 7157: 7153: 7150: 7146: 7142: 7133: 7129: 7126: 7122: 7118: 7115: 7110: 7106: 7102: 7099: 7097: 7088: 7083: 7082: 7079: 7070: 7066: 7063: 7059: 7055: 7046: 7042: 7039: 7035: 7031: 7028: 7023: 7019: 7015: 7012: 7010: 7001: 6996: 6995: 6979: 6954: 6903:Doppler shifts 6871: 6854:measured from 6850: 6794: 6784: 6754: 6744: 6699: 6690: 6678: 6664: 6652: 6640: 6637: 6622: 6619: 6615: 6609: 6605: 6601: 6590: 6581: 6574: 6570: 6566: 6563: 6526: 6521: 6511: 6505: 6500: 6496: 6491: 6487: 6459: 6455: 6451: 6448: 6440: 6436: 6431: 6425: 6421: 6415: 6410: 6406: 6381: 6377: 6373: 6368: 6365: 6320: 6314: 6311: 6285: 6273: 6263: 6257: 6254: 6225: 6221: 6215: 6211: 6202: 6197: 6194: 6191: 6159: 6156: 6148: 6143: 6140: 6137: 6133: 6129: 6099: 6098: 6089: 6087: 6076: 6070: 6066: 6062: 6057: 6054: 6016: 6015: 6006: 6004: 5993: 5987: 5984: 5978: 5975: 5972: 5923: 5919: 5916: 5913: 5910: 5908: 5906: 5903: 5900: 5897: 5896: 5893: 5890: 5887: 5884: 5882: 5880: 5877: 5874: 5871: 5870: 5801: 5796: 5792: 5788: 5784: 5781: 5778: 5776: 5773: 5769: 5766: 5763: 5762: 5758: 5754: 5750: 5746: 5743: 5741: 5738: 5734: 5731: 5728: 5727: 5623: 5618: 5614: 5610: 5606: 5603: 5600: 5598: 5595: 5591: 5588: 5587: 5583: 5579: 5575: 5571: 5568: 5566: 5563: 5559: 5556: 5555: 5534: 5533: 5524: 5522: 5511: 5505: 5502: 5499: 5495: 5491: 5484: 5480: 5449: 5448: 5439: 5437: 5426: 5422: 5418: 5414: 5411: 5408: 5405: 5374: 5370: 5366: 5348: 5339:phase velocity 5324: 5320: 5316: 5312: 5281: 5228: 5079:imaginary unit 5066: 5058: 5057: 5048: 5046: 5035: 5030: 5027: 5024: 5021: 5017: 5014: 5011: 5007: 5004: 5000: 4993: 4989: 4966:electric field 4957: 4954: 4875:wave impedance 4853: 4840: 4827: 4813: 4801: 4790: 4777: 4766: 4749: 4740: 4696: 4691: 4687: 4684: 4681: 4679: 4676: 4672: 4671: 4667: 4663: 4660: 4657: 4655: 4652: 4648: 4647: 4595: 4592: 4587: 4584: 4512: 4511: 4504: 4501: 4487: 4478: 4413:David Brewster 4386: 4383: 4335: 4332: 4325: 4292: 4286: 4277: 4273: 4264: 4260: 4257: 4254: 4249: 4240: 4236: 4227: 4223: 4220: 4217: 4211: 4202: 4185: 4167: 4161: 4152: 4148: 4139: 4135: 4132: 4129: 4124: 4115: 4111: 4102: 4098: 4095: 4092: 4086: 4083: 4074: 4057: 4040: 4008: 4004: 4001: 3997: 3987: 3983: 3980: 3975: 3971: 3967: 3962: 3958: 3941: 3933: 3930: 3912: 3903: 3841: 3830: 3802: 3797: 3792: 3788: 3775: 3771: 3768: 3763: 3759: 3747: 3743: 3740: 3735: 3731: 3724: 3721: 3679: 3674: 3669: 3664: 3660: 3656: 3653: 3624: 3617: 3607: 3596: 3582: 3575: 3553: 3541: 3537: 3534: 3529: 3525: 3521: 3512: 3508: 3505: 3500: 3496: 3484: 3480: 3477: 3472: 3468: 3464: 3458: 3455: 3453: 3445: 3441: 3440: 3437: 3425: 3421: 3418: 3413: 3409: 3405: 3396: 3392: 3389: 3384: 3380: 3368: 3364: 3361: 3356: 3352: 3348: 3339: 3335: 3332: 3327: 3323: 3316: 3313: 3311: 3303: 3299: 3298: 3295: 3283: 3279: 3276: 3271: 3267: 3263: 3254: 3250: 3247: 3242: 3238: 3226: 3222: 3219: 3214: 3210: 3206: 3200: 3197: 3195: 3187: 3183: 3182: 3179: 3167: 3163: 3160: 3155: 3151: 3147: 3138: 3134: 3131: 3126: 3122: 3110: 3106: 3103: 3098: 3094: 3090: 3081: 3077: 3074: 3069: 3065: 3058: 3055: 3053: 3045: 3041: 3040: 3002: 2997: 2971: 2966: 2962: 2956: 2951: 2925: 2920: 2804: 2778:complex-valued 2754: 2751: 2744: 2735: 2725: 2716: 2707: 2698: 2689: 2677: 2668: 2648: 2639: 2635: 2626: 2612: 2603: 2588: 2585: 2553: 2546: 2539:critical angle 2533: 2526: 2515:Main article: 2512: 2509: 2502: 2492: 2479: 2470: 2461: 2450:Main article: 2447: 2444: 2437: 2427: 2409: 2403: 2398: 2390: 2386: 2382: 2377: 2373: 2365: 2361: 2357: 2352: 2348: 2341: 2336: 2331: 2327: 2312: 2305: 2293: 2290: 2288: 2285: 2262: 2258: 2251: 2246: 2242: 2236: 2231: 2226: 2220: 2217: 2212: 2206: 2203: 2200: 2195: 2164: 2157: 2109: 2104: 2100: 2097: 2094: 2088: 2083: 2059: 2054: 2050: 2047: 2044: 2038: 2033: 2000: 1982: 1976: 1971: 1962: 1957: 1953: 1950: 1945: 1941: 1937: 1930: 1925: 1918: 1913: 1909: 1906: 1899: 1895: 1889: 1885: 1878: 1873: 1870: 1863: 1859: 1850: 1845: 1841: 1838: 1833: 1829: 1825: 1818: 1813: 1806: 1801: 1797: 1794: 1787: 1783: 1777: 1773: 1766: 1761: 1758: 1751: 1747: 1740: 1735: 1730: 1725: 1716: 1711: 1707: 1704: 1699: 1695: 1691: 1685: 1680: 1676: 1673: 1668: 1664: 1655: 1650: 1646: 1643: 1638: 1634: 1630: 1624: 1619: 1615: 1612: 1607: 1603: 1596: 1591: 1585: 1580: 1560: 1554: 1549: 1539: 1534: 1527: 1522: 1518: 1515: 1508: 1504: 1498: 1494: 1487: 1482: 1479: 1472: 1468: 1464: 1458: 1453: 1449: 1446: 1441: 1437: 1427: 1422: 1415: 1410: 1406: 1403: 1396: 1392: 1386: 1382: 1375: 1370: 1367: 1360: 1356: 1352: 1346: 1341: 1337: 1334: 1329: 1325: 1318: 1313: 1308: 1303: 1294: 1289: 1285: 1282: 1277: 1273: 1269: 1263: 1258: 1254: 1251: 1246: 1242: 1233: 1228: 1224: 1221: 1216: 1212: 1208: 1202: 1197: 1193: 1190: 1185: 1181: 1174: 1169: 1163: 1158: 1133: 1117: 1109: 1105: 1099: 1095: 1089: 1084: 1080: 1066: 1057: 1047: 1039: 1032: 1016: 1007: 991: 986: 981: 972: 967: 963: 960: 955: 951: 947: 941: 936: 932: 929: 924: 920: 911: 906: 902: 899: 894: 890: 886: 880: 875: 871: 868: 863: 859: 852: 847: 841: 836: 811: 806: 801: 792: 787: 783: 780: 775: 771: 767: 761: 756: 752: 749: 744: 740: 731: 726: 722: 719: 714: 710: 706: 700: 695: 691: 688: 683: 679: 672: 667: 661: 656: 619:transmissivity 568: 565: 530: 524: 519: 515: 512: 507: 503: 499: 493: 488: 484: 481: 476: 472: 447: 441: 436: 432: 426: 421: 403: 394: 385: 354: 345: 319: 316: 241:Main article: 238: 235: 194: 185: 174: 171: 71: 70: 61: 60: 52: 51: 50: 49: 48: 26: 9: 6: 4: 3: 2: 17008: 16997: 16994: 16992: 16989: 16987: 16984: 16982: 16979: 16977: 16974: 16972: 16969: 16968: 16966: 16956: 16951: 16946: 16945: 16942: 16934: 16931: 16928: 16925: 16922: 16919: 16916: 16913: 16910: 16907: 16905: 16902: 16899: 16896: 16895: 16887: 16886:0-07-051400-3 16883: 16879: 16876: 16873: 16869: 16866: 16862: 16856: 16851: 16850: 16843: 16839: 16833: 16829: 16824: 16820: 16814: 16810: 16805: 16801: 16795: 16790: 16789: 16782: 16781: 16774: 16771: 16763: 16753: 16752:editing guide 16747: 16743: 16738: 16729: 16728: 16717: 16716: 16711: 16708: 16705: 16697: 16693: 16686: 16682: 16678: 16675: 16674:0-07-032330-5 16671: 16667: 16663: 16660: 16659:0-321-18878-0 16656: 16652: 16648: 16645: 16644:0-201-11609-X 16641: 16637: 16633: 16630: 16629:1 (1866) 16622: 16614: 16611: 16607: 16603: 16599: 16596: 16592: 16589: 16588:0-226-07886-8 16585: 16581: 16577: 16574: 16573: 16568: 16567: 16553: 16534: 16530: 16524: 16516: 16512: 16508: 16504: 16500: 16496: 16492: 16488: 16481: 16472: 16461: 16457: 16445: 16439: 16414: 16401: 16394: 16390: 16375: 16362: 16345: 16320: 16311: 16294: 16272: 16270: 16262: 16258: 16253: 16248: 16245:postscript", 16228: 16222: 16205: 16198: 16186: 16176: 16161: 16157: 16154:D. Brewster, 16151: 16138: 16129: 16122: 16109: 16100: 16091: 16082: 16073: 16064: 16055: 16046: 16037: 16028: 16015: 16002: 16000: 15992: 15988: 15984: 15981: 15975: 15973: 15963: 15955: 15949: 15945: 15944:10.1081/E-EOE 15941: 15937: 15930: 15921: 15912: 15908: 15893: 15887: 15881: 15876: 15866: 15858: 15852: 15843: 15838: 15832: 15825: 15821: 15813: 15809: 15808: 15801: 15797: 15787: 15784: 15782: 15779: 15777: 15774: 15772: 15769: 15767: 15764: 15762: 15759: 15757: 15754: 15751: 15750:Fresnel rhomb 15748: 15746: 15743: 15741: 15738: 15736: 15733: 15731: 15728: 15727: 15721: 15719: 15715: 15711: 15707: 15703: 15699: 15695: 15691: 15690: 15684: 15669: 15650: 15642: 15641: 15632: 15623: 15618: 15617: 15612: 15611: 15602: 15596: 15591: 15590: 15585: 15584: 15575: 15566: 15560: 15555: 15554: 15549: 15548: 15536: 15529: 15522: 15520: 15501: 15497: 15492: 15486: 15482: 15475: 15472: 15469: 15460: 15452: 15451: 15448: 15439: 15420: 15408: 15393: 15374: 15361: 15351: 15338: 15330: 15329: 15317: 15298: 15279: 15260: 15248: 15247: 15246:complementary 15238: 15229: 15218: 15215: 15211: 15201: 15194: 15192: 15178: 15172: 15167: 15155: 15151: 15148: 15143: 15139: 15135: 15126: 15122: 15119: 15114: 15110: 15098: 15094: 15091: 15086: 15082: 15078: 15069: 15065: 15062: 15057: 15053: 15046: 15041: 15032: 15024: 15023: 15016: 15009: 15007: 14991: 14986: 14974: 14970: 14967: 14962: 14958: 14954: 14945: 14941: 14938: 14933: 14929: 14917: 14913: 14910: 14905: 14901: 14897: 14888: 14884: 14881: 14876: 14872: 14865: 14860: 14851: 14843: 14842: 14839: 14832: 14825: 14823: 14809: 14800: 14796: 14792: 14787: 14783: 14775: 14771: 14767: 14761: 14752: 14744: 14743: 14736: 14729: 14727: 14708: 14704: 14700: 14695: 14691: 14683: 14679: 14675: 14670: 14666: 14659: 14650: 14642: 14641: 14634: 14627: 14625: 14606: 14602: 14598: 14593: 14589: 14581: 14577: 14573: 14567: 14558: 14550: 14549: 14542: 14535: 14533: 14514: 14510: 14506: 14501: 14497: 14489: 14485: 14481: 14476: 14472: 14465: 14456: 14448: 14447: 14444: 14437: 14430: 14428: 14414: 14401: 14397: 14394: 14389: 14385: 14381: 14372: 14368: 14365: 14360: 14356: 14344: 14340: 14337: 14332: 14328: 14324: 14318: 14309: 14301: 14300: 14293: 14286: 14284: 14261: 14257: 14254: 14249: 14245: 14241: 14232: 14228: 14225: 14220: 14216: 14204: 14200: 14197: 14192: 14188: 14184: 14175: 14171: 14168: 14163: 14159: 14152: 14143: 14135: 14134: 14127: 14120: 14118: 14094: 14090: 14087: 14082: 14078: 14074: 14065: 14061: 14058: 14053: 14049: 14037: 14033: 14030: 14025: 14021: 14017: 14011: 14002: 13994: 13993: 13986: 13979: 13977: 13954: 13950: 13947: 13942: 13938: 13934: 13925: 13921: 13918: 13913: 13909: 13897: 13893: 13890: 13885: 13881: 13877: 13868: 13864: 13861: 13856: 13852: 13845: 13836: 13828: 13827: 13824: 13819: 13815: 13814: 13809: 13808: 13803: 13802: 13797: 13796: 13779: 13770: 13766: 13762: 13755: 13751: 13745: 13740: 13736: 13723: 13709: 13705: 13701: 13694: 13690: 13684: 13679: 13675: 13665: 13656: 13652: 13636: 13628: 13625: 13620: 13615: 13612: 13604: 13603: 13598: 13597: 13586: 13584: 13580: 13579: 13574: 13573: 13568: 13567: 13562: 13561: 13556: 13555: 13550: 13549: 13537: 13527: 13519: 13518: 13513: 13512: 13501: 13487: 13484: 13481: 13478: 13475: 13450: 13446: 13442: 13437: 13433: 13424: 13421: 13416: 13413: 13389: 13385: 13381: 13376: 13372: 13363: 13360: 13355: 13352: 13343: 13339: 13329: 13322: 13320: 13302: 13297: 13287: 13283: 13280: 13275: 13271: 13267: 13258: 13254: 13251: 13246: 13242: 13237: 13225: 13221: 13218: 13209: 13205: 13202: 13197: 13193: 13187: 13183: 13179: 13173: 13161: 13157: 13154: 13143: 13139: 13136: 13125: 13121: 13113: 13109: 13099: 13094: 13082: 13078: 13075: 13070: 13066: 13062: 13053: 13049: 13046: 13041: 13037: 13025: 13021: 13018: 13013: 13009: 13005: 12999: 12994: 12985: 12977: 12976: 12973: 12966: 12959: 12957: 12939: 12934: 12924: 12920: 12917: 12912: 12908: 12904: 12895: 12891: 12888: 12883: 12879: 12874: 12862: 12858: 12855: 12846: 12842: 12839: 12834: 12830: 12824: 12820: 12816: 12810: 12798: 12794: 12791: 12780: 12776: 12773: 12762: 12758: 12750: 12746: 12736: 12731: 12719: 12715: 12712: 12707: 12703: 12699: 12690: 12686: 12683: 12678: 12674: 12662: 12658: 12655: 12650: 12646: 12642: 12636: 12631: 12622: 12614: 12613: 12610: 12600: 12590: 12589: 12584: 12583: 12578: 12573: 12566: 12559: 12557: 12539: 12534: 12524: 12520: 12517: 12512: 12508: 12504: 12495: 12491: 12488: 12483: 12479: 12474: 12459: 12455: 12452: 12443: 12439: 12436: 12431: 12427: 12421: 12417: 12404: 12397: 12388: 12384: 12381: 12378: 12369: 12361: 12360: 12357: 12350: 12343: 12341: 12323: 12318: 12308: 12304: 12301: 12296: 12292: 12288: 12279: 12275: 12272: 12267: 12263: 12258: 12243: 12239: 12236: 12227: 12223: 12220: 12215: 12211: 12205: 12201: 12188: 12181: 12172: 12168: 12165: 12162: 12153: 12145: 12144: 12141: 12134: 12130: 12121: 12117: 12116: 12110: 12108: 12104: 12088: 12081: 12079: 12063: 12058: 12046: 12042: 12039: 12034: 12030: 12026: 12017: 12013: 12010: 12005: 12001: 11989: 11985: 11982: 11977: 11973: 11969: 11960: 11956: 11953: 11948: 11944: 11937: 11932: 11923: 11915: 11914: 11911: 11904: 11897: 11895: 11879: 11874: 11862: 11858: 11855: 11850: 11846: 11842: 11833: 11829: 11826: 11821: 11817: 11805: 11801: 11798: 11793: 11789: 11785: 11776: 11772: 11769: 11764: 11760: 11753: 11748: 11739: 11731: 11730: 11727: 11725: 11724: 11719: 11718: 11713: 11712: 11706: 11703: 11695: 11691: 11681: 11675: 11669: 11655: 11651: 11642: 11638: 11624: 11618: 11613: 11608: 11602: 11588: 11582: 11568: 11562: 11556: 11551: 11546: 11540: 11533: 11523: 11496: 11495: 11490: 11489: 11478: 11476: 11471: 11467: 11466: 11461: 11460: 11455: 11454: 11449: 11448: 11442: 11435: 11419: 11403: 11383: 11377: 11367: 11360: 11358: 11344: 11335: 11331: 11327: 11322: 11318: 11310: 11306: 11302: 11296: 11287: 11279: 11278: 11275: 11268: 11261: 11259: 11240: 11236: 11232: 11227: 11223: 11215: 11211: 11207: 11202: 11198: 11191: 11182: 11174: 11173: 11170: 11166: 11144: 11135: 11128: 11126: 11112: 11099: 11095: 11092: 11087: 11083: 11079: 11070: 11066: 11063: 11058: 11054: 11042: 11038: 11035: 11030: 11026: 11022: 11016: 11007: 10999: 10998: 10995: 10988: 10981: 10979: 10956: 10952: 10949: 10944: 10940: 10936: 10927: 10923: 10920: 10915: 10911: 10899: 10895: 10892: 10887: 10883: 10879: 10870: 10866: 10863: 10858: 10854: 10847: 10838: 10830: 10829: 10826: 10817: 10808: 10798: 10791: 10789: 10771: 10761: 10755: 10751: 10746: 10744: 10733: 10727: 10723: 10719: 10714: 10710: 10696: 10692: 10689: 10680: 10675: 10673: 10662: 10658: 10655: 10646: 10642: 10633: 10629: 10626: 10615: 10614: 10611: 10609: 10608: 10603: 10602: 10597: 10596: 10586: 10579: 10577: 10563: 10559: 10556: 10553: 10529: 10509: 10505: 10503: 10492: 10488: 10479: 10465: 10461: 10458: 10449: 10445: 10443: 10432: 10428: 10425: 10416: 10412: 10403: 10399: 10396: 10387: 10371: 10370: 10367: 10364: 10358: 10348: 10341: 10339: 10321: 10312: 10296: 10292: 10285: 10281: 10275: 10271: 10266: 10264: 10253: 10239: 10223: 10219: 10212: 10208: 10202: 10198: 10193: 10191: 10180: 10166: 10150: 10146: 10140: 10136: 10131: 10129: 10118: 10106: 10105: 10102: 10096: 10075: 10062: 10052: 10043: 10037: 10031: 10028: 10020: 10015: 10005: 9999: 9990: 9983: 9976: 9967: 9957: 9950: 9948: 9930: 9921: 9905: 9901: 9894: 9890: 9886: 9884: 9873: 9859: 9843: 9839: 9832: 9828: 9824: 9822: 9811: 9797: 9781: 9777: 9773: 9771: 9760: 9748: 9747: 9744: 9741: 9732: 9723: 9713: 9700: 9690: 9681: 9676: 9668: 9662: 9652: 9629: 9610: 9590: 9582: 9573: 9566: 9564: 9550: 9541: 9537: 9533: 9528: 9524: 9516: 9512: 9508: 9502: 9493: 9485: 9484: 9481: 9474: 9467: 9465: 9446: 9442: 9438: 9433: 9429: 9421: 9417: 9413: 9408: 9404: 9397: 9388: 9380: 9379: 9376: 9372: 9350: 9341: 9334: 9332: 9318: 9305: 9301: 9298: 9293: 9289: 9285: 9276: 9272: 9269: 9264: 9260: 9248: 9244: 9241: 9236: 9232: 9228: 9222: 9213: 9205: 9204: 9201: 9194: 9187: 9185: 9162: 9158: 9155: 9150: 9146: 9142: 9133: 9129: 9126: 9121: 9117: 9105: 9101: 9098: 9093: 9089: 9085: 9076: 9072: 9069: 9064: 9060: 9053: 9044: 9036: 9035: 9032: 9023: 9014: 9004: 8997: 8995: 8977: 8967: 8963: 8960: 8951: 8945: 8941: 8936: 8934: 8923: 8919: 8916: 8907: 8901: 8897: 8893: 8884: 8880: 8877: 8872: 8868: 8854: 8849: 8847: 8836: 8832: 8829: 8818: 8817: 8814: 8812: 8811: 8806: 8805: 8800: 8799: 8789: 8782: 8780: 8766: 8762: 8759: 8756: 8732: 8712: 8708: 8705: 8696: 8692: 8690: 8679: 8675: 8672: 8663: 8659: 8650: 8646: 8643: 8634: 8620: 8616: 8614: 8603: 8599: 8590: 8574: 8573: 8570: 8567: 8561: 8556: 8547: 8540: 8538: 8520: 8511: 8495: 8491: 8484: 8480: 8474: 8470: 8465: 8463: 8452: 8438: 8422: 8418: 8411: 8407: 8401: 8397: 8392: 8390: 8379: 8365: 8349: 8345: 8339: 8335: 8330: 8328: 8317: 8305: 8304: 8301: 8295: 8291: 8278: 8265: 8255: 8246: 8237: 8230: 8223: 8214: 8208: 8202: 8196: 8191: 8187: 8178: 8171: 8169: 8151: 8142: 8126: 8122: 8115: 8111: 8107: 8105: 8094: 8080: 8064: 8060: 8053: 8049: 8045: 8043: 8032: 8020: 8019: 8016: 8009: 8002: 8000: 7986: 7977: 7961: 7957: 7953: 7944: 7936: 7935: 7932: 7929: 7924: 7923: 7917: 7907: 7898: 7892: 7886: 7880: 7875: 7867: 7857: 7850: 7848: 7834: 7824: 7820: 7817: 7814: 7811: 7806: 7802: 7798: 7791: 7775: 7768: 7752: 7745: 7720: 7716: 7713: 7710: 7702: 7701: 7698: 7691: 7684: 7682: 7664: 7651: 7647: 7644: 7641: 7636: 7632: 7628: 7619: 7615: 7612: 7609: 7604: 7600: 7593: 7590: 7588: 7579: 7550: 7546: 7543: 7540: 7537: 7528: 7524: 7521: 7518: 7512: 7507: 7503: 7499: 7497: 7488: 7459: 7455: 7452: 7449: 7446: 7437: 7433: 7430: 7427: 7421: 7416: 7412: 7408: 7406: 7397: 7373: 7372: 7369: 7367: 7366: 7361: 7341: 7328: 7324: 7321: 7316: 7312: 7302: 7293: 7289: 7286: 7281: 7277: 7264: 7261: 7259: 7242: 7238: 7235: 7227: 7218: 7214: 7211: 7200: 7195: 7191: 7187: 7185: 7155: 7151: 7148: 7140: 7131: 7127: 7124: 7113: 7108: 7104: 7100: 7098: 7068: 7064: 7061: 7053: 7044: 7040: 7037: 7026: 7021: 7017: 7013: 7011: 6984: 6978: 6968: 6959: 6953: 6939: 6934: 6927: 6922: 6916: 6914: 6913: 6908: 6904: 6899: 6897: 6892: 6887: 6882: 6870: 6864: 6858: 6849: 6843: 6837: 6831: 6826: 6821: 6815: 6809: 6803: 6793: 6783: 6766: 6753: 6743: 6733: 6723: 6716: 6712: 6698: 6689: 6681: 6677: 6667: 6663: 6655: 6651: 6645: 6636: 6620: 6617: 6613: 6607: 6603: 6599: 6588: 6572: 6568: 6564: 6561: 6553: 6524: 6519: 6509: 6503: 6498: 6494: 6489: 6485: 6476: 6473:known as the 6457: 6449: 6446: 6438: 6434: 6429: 6423: 6419: 6413: 6408: 6404: 6379: 6375: 6371: 6366: 6363: 6354: 6350: 6349: 6318: 6312: 6309: 6299: 6283: 6271: 6261: 6255: 6252: 6223: 6219: 6213: 6209: 6195: 6192: 6189: 6157: 6154: 6141: 6138: 6135: 6131: 6127: 6115: 6114: 6108: 6106: 6097: 6090: 6088: 6074: 6068: 6064: 6060: 6055: 6052: 6045: 6044: 6041: 6035: 6014: 6007: 6005: 5991: 5985: 5982: 5976: 5973: 5970: 5963: 5962: 5959: 5956: 5950: 5921: 5917: 5914: 5911: 5909: 5904: 5901: 5898: 5891: 5888: 5885: 5883: 5878: 5875: 5872: 5861:), we obtain 5860: 5859: 5854: 5846: 5839: 5832: 5826: 5820: 5799: 5790: 5782: 5779: 5777: 5767: 5764: 5752: 5744: 5742: 5732: 5729: 5716: 5710: 5704: 5698: 5685: 5682: 5672: 5660: 5657: 5647: 5638: 5621: 5612: 5604: 5601: 5599: 5589: 5577: 5569: 5567: 5557: 5545: 5541: 5540:Faraday's law 5532: 5525: 5523: 5509: 5500: 5493: 5489: 5469: 5468: 5465: 5464: 5463: 5457: 5447: 5440: 5438: 5424: 5420: 5416: 5412: 5409: 5406: 5403: 5396: 5395: 5392: 5372: 5368: 5364: 5347: 5341: 5340: 5336:known as the 5322: 5318: 5314: 5310: 5299: 5294: 5288: 5284: 5273: 5272: 5268:, the field ( 5263: 5257: 5252: 5247: 5244: 5238: 5235: 5231: 5220: 5219: 5214: 5211: 5207: 5204:. So a phase 5202: 5196: 5192: 5185: 5175: 5171: 5165: 5161:, we replace 5160: 5157:by the angle 5156: 5151: 5149: 5145: 5139: 5133: 5128: 5123: 5118: 5113: 5108: 5103: 5098: 5090: 5085: 5080: 5075: 5069: 5056: 5049: 5047: 5033: 5025: 5022: 5019: 5012: 5002: 4998: 4978: 4977: 4974: 4973:has the form 4971: 4967: 4963: 4953: 4951: 4947: 4946: 4943: 4936: 4927: 4922: 4912: 4906: 4896: 4890: 4884: 4876: 4867: 4863: 4858: 4852: 4848: 4839: 4834: 4833:metamaterials 4826: 4821: 4820:ferromagnetic 4812: 4806: 4800: 4796: 4789: 4785:permeability 4784: 4776: 4772: 4765: 4760: 4756: 4748: 4739: 4734: 4733: 4728: 4727: 4721: 4715: 4694: 4685: 4682: 4680: 4661: 4658: 4656: 4637: 4629: 4625: 4621: 4617: 4609: 4605: 4601: 4591: 4583: 4581: 4580: 4573: 4571: 4570:birefringence 4567: 4563: 4562: 4557: 4556: 4551: 4550: 4544: 4542: 4538: 4534: 4529: 4527: 4526: 4517: 4516:Fresnel rhomb 4509: 4505: 4502: 4498: 4497: 4496: 4494: 4486: 4477: 4471: 4469: 4465: 4461: 4457: 4453: 4448: 4446: 4442: 4438: 4434: 4428: 4424: 4422: 4418: 4414: 4410: 4406: 4402: 4398: 4392: 4382: 4380: 4375: 4373: 4369: 4365: 4361: 4357: 4352: 4350: 4346: 4341: 4331: 4324: 4316: 4312: 4308: 4303: 4290: 4275: 4271: 4262: 4255: 4252: 4238: 4234: 4225: 4218: 4215: 4209: 4200: 4184: 4178: 4165: 4150: 4146: 4137: 4130: 4127: 4113: 4109: 4100: 4093: 4090: 4084: 4081: 4072: 4056: 4039: 4006: 4002: 3999: 3995: 3985: 3981: 3978: 3973: 3969: 3965: 3960: 3956: 3940: 3929: 3927: 3923: 3919: 3911: 3902: 3897: 3891: 3886: 3874: 3869: 3865: 3860: 3854: 3840: 3829: 3819: 3800: 3790: 3773: 3769: 3766: 3761: 3757: 3745: 3741: 3738: 3733: 3729: 3722: 3719: 3711: 3710:multiplied by 3707: 3703: 3699: 3690: 3677: 3672: 3662: 3654: 3651: 3642: 3636: 3630: 3623: 3616: 3606: 3595: 3581: 3574: 3568: 3551: 3539: 3535: 3532: 3527: 3523: 3519: 3510: 3506: 3503: 3498: 3494: 3482: 3478: 3475: 3470: 3466: 3462: 3456: 3454: 3443: 3435: 3423: 3419: 3416: 3411: 3407: 3403: 3394: 3390: 3387: 3382: 3378: 3366: 3362: 3359: 3354: 3350: 3346: 3337: 3333: 3330: 3325: 3321: 3314: 3312: 3301: 3293: 3281: 3277: 3274: 3269: 3265: 3261: 3252: 3248: 3245: 3240: 3236: 3224: 3220: 3217: 3212: 3208: 3204: 3198: 3196: 3185: 3177: 3165: 3161: 3158: 3153: 3149: 3145: 3136: 3132: 3129: 3124: 3120: 3108: 3104: 3101: 3096: 3092: 3088: 3079: 3075: 3072: 3067: 3063: 3056: 3054: 3043: 3029: 3027: 3021: 2995: 2964: 2960: 2949: 2918: 2909: 2904: 2902: 2898: 2893: 2888: 2884: 2880: 2876: 2871: 2865: 2859: 2854: 2850: 2845: 2841:polarization 2840: 2835: 2830: 2821: 2813: 2809: 2803: 2797: 2791: 2785: 2779: 2775: 2771: 2767: 2764: 2760: 2750: 2743: 2734: 2724: 2715: 2706: 2697: 2688: 2682: 2676: 2667: 2661: 2646: 2637: 2633: 2624: 2611: 2602: 2595: 2587:45° incidence 2584: 2580: 2574: 2570:for all real 2567: 2561: 2552: 2545: 2540: 2532: 2525: 2518: 2508: 2501: 2491: 2486: 2478: 2469: 2460: 2453: 2443: 2436: 2426: 2420: 2407: 2401: 2396: 2388: 2384: 2380: 2375: 2371: 2363: 2359: 2355: 2350: 2346: 2339: 2334: 2329: 2325: 2311: 2304: 2299: 2287:Special cases 2284: 2282: 2278: 2273: 2260: 2256: 2244: 2240: 2229: 2224: 2218: 2215: 2210: 2193: 2184: 2180: 2176: 2170: 2163: 2156: 2150: 2145: 2139: 2133: 2129: 2123: 2102: 2098: 2095: 2092: 2081: 2052: 2048: 2045: 2042: 2031: 2022: 2018: 2013: 2011: 2007: 1999: 1993: 1980: 1974: 1969: 1955: 1951: 1948: 1943: 1939: 1935: 1928: 1923: 1911: 1907: 1904: 1897: 1893: 1887: 1883: 1876: 1871: 1868: 1861: 1857: 1843: 1839: 1836: 1831: 1827: 1823: 1816: 1811: 1799: 1795: 1792: 1785: 1781: 1775: 1771: 1764: 1759: 1756: 1749: 1745: 1738: 1733: 1728: 1723: 1709: 1705: 1702: 1697: 1693: 1689: 1678: 1674: 1671: 1666: 1662: 1648: 1644: 1641: 1636: 1632: 1628: 1617: 1613: 1610: 1605: 1601: 1594: 1589: 1578: 1558: 1552: 1547: 1537: 1532: 1520: 1516: 1513: 1506: 1502: 1496: 1492: 1485: 1480: 1477: 1470: 1466: 1462: 1451: 1447: 1444: 1439: 1435: 1425: 1420: 1408: 1404: 1401: 1394: 1390: 1384: 1380: 1373: 1368: 1365: 1358: 1354: 1350: 1339: 1335: 1332: 1327: 1323: 1316: 1311: 1306: 1301: 1287: 1283: 1280: 1275: 1271: 1267: 1256: 1252: 1249: 1244: 1240: 1226: 1222: 1219: 1214: 1210: 1206: 1195: 1191: 1188: 1183: 1179: 1172: 1167: 1156: 1145: 1140: 1132: 1115: 1107: 1103: 1097: 1093: 1087: 1082: 1078: 1065: 1056: 1050: 1046: 1038: 1031: 1025: 1023: 1015: 1006: 989: 984: 979: 965: 961: 958: 953: 949: 945: 934: 930: 927: 922: 918: 904: 900: 897: 892: 888: 884: 873: 869: 866: 861: 857: 850: 845: 834: 825: 809: 804: 799: 785: 781: 778: 773: 769: 765: 754: 750: 747: 742: 738: 724: 720: 717: 712: 708: 704: 693: 689: 686: 681: 677: 670: 665: 654: 645: 640: 638: 634: 629: 624: 620: 616: 615: 614:transmittance 609: 604: 600: 596: 595: 590: 581: 573: 564: 562: 558: 554: 550: 546: 541: 528: 517: 513: 510: 505: 501: 497: 486: 482: 479: 474: 470: 461: 445: 434: 430: 419: 410: 402: 393: 384: 379: 374: 368: 362: 353: 344: 338: 333: 324: 318:Configuration 315: 313: 307: 301: 299: 291: 287: 279: 275: 274: 268: 266: 262: 258: 249: 244: 234: 232: 228: 223: 221: 217: 213: 209: 205: 201: 193: 184: 180: 170: 168: 164: 160: 156: 150: 120: 117: 113: 109: 105: 101: 97: 87: 83: 79: 75: 65: 56: 43: 37: 33: 19: 16877: 16867: 16848: 16827: 16808: 16787: 16766: 16760:October 2014 16757: 16745: 16714: 16695: 16684: 16665: 16650: 16635: 16620: 16601: 16594: 16579: 16570: 16552: 16532: 16523: 16490: 16486: 16480: 16471: 16443: 16438: 16413: 16400: 16392: 16388: 16374: 16361: 16344: 16319: 16310: 16293: 16226: 16221: 16204: 16184: 16175: 16159: 16150: 16137: 16127: 16121: 16108: 16099: 16090: 16081: 16072: 16063: 16054: 16045: 16036: 16027: 16014: 15962: 15935: 15929: 15920: 15911: 15891: 15885: 15879: 15871: 15865: 15856: 15850: 15836: 15830: 15823: 15816: 15805: 15800: 15717: 15714:elasticities 15713: 15697: 15693: 15687: 15685: 15667: 15648: 15638: 15630: 15621: 15614: 15608: 15600: 15594: 15587: 15581: 15573: 15564: 15558: 15551: 15545: 15542: 15534: 15523: 15437: 15418: 15391: 15372: 15359: 15349: 15336: 15326: 15315: 15296: 15277: 15258: 15244: 15236: 15227: 15224: 15213: 15209: 15206: 15195: 15010: 14837: 14826: 14730: 14628: 14536: 14442: 14431: 14287: 14121: 13980: 13817: 13811: 13805: 13799: 13793: 13663: 13654: 13600: 13594: 13592: 13576: 13570: 13564: 13558: 13552: 13546: 13535: 13525: 13515: 13509: 13507: 13344: 13337: 13334: 13323: 12971: 12960: 12598: 12586: 12580: 12576: 12574: 12571: 12560: 12355: 12344: 12132: 12128: 12119: 12113: 12111: 12107:transmission 12106: 12102: 12093: 12082: 11909: 11898: 11723:reflectivity 11721: 11715: 11709: 11707: 11701: 11693: 11689: 11679: 11673: 11667: 11653: 11649: 11640: 11636: 11622: 11616: 11606: 11600: 11586: 11580: 11566: 11560: 11554: 11549: 11544: 11538: 11531: 11521: 11492: 11486: 11484: 11474: 11469: 11463: 11457: 11451: 11445: 11443: 11433: 11417: 11401: 11381: 11375: 11372: 11361: 11273: 11262: 11150: 11142: 11140: 11129: 10993: 10982: 10815: 10806: 10804:Solving for 10803: 10792: 10605: 10599: 10593: 10591: 10580: 10362: 10356: 10353: 10342: 10086: 10073: 10060: 10050: 10041: 10035: 10032: 10026: 10021:polarization 10018: 10013: 10003: 9997: 9988: 9981: 9974: 9965: 9962: 9951: 9739: 9730: 9721: 9711: 9698: 9688: 9679: 9674: 9672: 9666: 9650: 9627: 9608: 9588: 9580: 9578: 9567: 9479: 9468: 9356: 9348: 9346: 9335: 9199: 9188: 9021: 9012: 9009: 8998: 8808: 8802: 8796: 8794: 8783: 8565: 8559: 8552: 8541: 8293: 8289: 8276: 8263: 8253: 8244: 8235: 8228: 8221: 8212: 8206: 8200: 8194: 8189: 8185: 8183: 8172: 8014: 8003: 7927: 7920: 7915: 7905: 7896: 7890: 7884: 7878: 7873: 7871: 7865: 7851: 7696: 7685: 7363: 7360:dot products 6982: 6976: 6966: 6957: 6951: 6937: 6932: 6925: 6920: 6917: 6910: 6906: 6900: 6895: 6890: 6888:(reserving 6885: 6880: 6868: 6862: 6856: 6847: 6841: 6835: 6829: 6819: 6813: 6807: 6801: 6791: 6781: 6764: 6751: 6741: 6731: 6721: 6714: 6710: 6706: 6696: 6687: 6679: 6675: 6665: 6661: 6653: 6649: 6639:Wave vectors 6552:non-magnetic 6551: 6352: 6346: 6298:non-magnetic 6297: 6111: 6109: 6104: 6103:This is the 6102: 6091: 6025: 6019: 6008: 5954: 5948: 5856: 5852: 5844: 5837: 5830: 5824: 5818: 5714: 5708: 5702: 5696: 5683: 5680: 5670: 5658: 5655: 5645: 5639: 5537: 5526: 5460: 5455: 5452: 5441: 5387:Solving for 5345: 5337: 5297: 5292: 5286: 5279: 5269: 5261: 5255: 5250: 5248: 5242: 5236: 5233: 5226: 5216: 5209: 5205: 5200: 5194: 5190: 5183: 5173: 5169: 5163: 5158: 5152: 5147: 5143: 5137: 5131: 5126: 5121: 5111: 5101: 5083: 5073: 5064: 5061: 5050: 4969: 4959: 4949: 4939: 4937: 4925: 4920: 4910: 4904: 4902:in terms of 4894: 4888: 4882: 4865: 4859: 4850: 4846: 4837: 4824: 4810: 4807: 4798: 4794: 4787: 4782: 4774: 4770: 4763: 4754: 4746: 4737: 4732:permeability 4730: 4726:permittivity 4724: 4719: 4713: 4627: 4623: 4619: 4615: 4597: 4589: 4577: 4574: 4559: 4553: 4547: 4545: 4530: 4519: 4515: 4513: 4484: 4475: 4472: 4463: 4459: 4455: 4449: 4447:transverse. 4444: 4430: 4426: 4416: 4409:polarization 4408: 4400: 4394: 4376: 4353: 4337: 4322: 4310: 4306: 4304: 4182: 4179: 4054: 4037: 3948:, if we put 3938: 3935: 3921: 3917: 3909: 3900: 3896:phase angles 3889: 3870: 3863: 3858: 3852: 3838: 3827: 3817: 3709: 3701: 3691: 3640: 3634: 3631: 3621: 3614: 3604: 3593: 3579: 3572: 3569: 3030: 3019: 2905: 2900: 2896: 2891: 2886: 2882: 2878: 2874: 2869: 2863: 2857: 2852: 2848: 2843: 2838: 2833: 2828: 2826: 2801: 2795: 2789: 2783: 2756: 2741: 2732: 2722: 2713: 2704: 2695: 2686: 2683: 2674: 2665: 2662: 2609: 2600: 2593: 2590: 2578: 2572: 2565: 2550: 2543: 2538: 2530: 2523: 2520: 2499: 2489: 2476: 2467: 2458: 2455: 2434: 2424: 2421: 2309: 2302: 2295: 2274: 2182: 2178: 2174: 2171: 2161: 2160:= cos  2154: 2143: 2137: 2127: 2124: 2014: 1997: 1994: 1143: 1130: 1063: 1054: 1044: 1036: 1029: 1026: 1013: 1004: 641: 636: 632: 627: 622: 618: 612: 607: 602: 599:reflectivity 598: 592: 586: 556: 542: 400: 391: 382: 372: 366: 360: 351: 342: 336: 329: 305: 302: 297: 289: 285: 271: 269: 257:polarization 254: 224: 220:phase shifts 215: 211: 207: 191: 182: 176: 166: 162: 159:polarization 99: 95: 93: 85: 77: 74:near-grazing 36:Fresnel lens 16872:R.G. Lerner 15834:instead of 15643:) will give 12122:, i.e. the 11477:incidence. 11444:Comparing ( 9031:, yielding 6886:transmitted 6884:stands for 5089:wave vector 4604:homogeneous 4500:solutions), 4360:soap bubble 2149:dot product 2006:Snell's law 594:reflectance 551:, as shown 460:Snell's law 265:unpolarized 212:transmitted 16965:Categories 16900:– Wolfram. 16744:" section 16604:, Oxford, 15991:Lecture 12 15903:References 15706:MacCullagh 15662:instead of 13667:, so that 13605:)) yields 13342: ). 12597:cos  11612:irradiance 11494:irradiance 10825:, we find 9669:components 8186:transverse 7868:components 6825:roman type 5097:wavenumber 4945:sinusoidal 4926:admittance 4586:Derivation 4456:tangential 4415:. But the 4356:iridescent 3702:divided by 3698:irradiance 2774:amplitudes 2759:photometer 2564:sin  2153:cos  2136:cos  2021:irradiance 561:irradiance 332:plane wave 231:plane wave 204:refraction 200:reflection 84:block the 16909:FreeSnell 16515:118838757 16132:chapt. 4. 15980:main site 15694:densities 15574:inversely 15476:⁡ 15461:θ 15331:) becomes 15156:θ 15152:⁡ 15127:θ 15123:⁡ 15099:θ 15095:⁡ 15079:− 15070:θ 15066:⁡ 14975:θ 14971:⁡ 14946:θ 14942:⁡ 14918:θ 14914:⁡ 14898:− 14889:θ 14885:⁡ 14676:− 14482:− 14402:θ 14398:⁡ 14373:θ 14369:⁡ 14345:θ 14341:⁡ 14262:θ 14258:⁡ 14233:θ 14229:⁡ 14205:θ 14201:⁡ 14185:− 14176:θ 14172:⁡ 14095:θ 14091:⁡ 14066:θ 14062:⁡ 14038:θ 14034:⁡ 13955:θ 13951:⁡ 13926:θ 13922:⁡ 13898:θ 13894:⁡ 13878:− 13869:θ 13865:⁡ 13767:μ 13706:μ 13629:μ 13288:θ 13284:⁡ 13259:θ 13255:⁡ 13226:θ 13222:⁡ 13210:θ 13206:⁡ 13162:θ 13158:⁡ 13144:θ 13140:⁡ 13083:θ 13079:⁡ 13054:θ 13050:⁡ 13026:θ 13022:⁡ 12925:θ 12921:⁡ 12896:θ 12892:⁡ 12863:θ 12859:⁡ 12847:θ 12843:⁡ 12799:θ 12795:⁡ 12781:θ 12777:⁡ 12720:θ 12716:⁡ 12691:θ 12687:⁡ 12663:θ 12659:⁡ 12525:θ 12521:⁡ 12496:θ 12492:⁡ 12460:θ 12456:⁡ 12444:θ 12440:⁡ 12385:− 12309:θ 12305:⁡ 12280:θ 12276:⁡ 12244:θ 12240:⁡ 12228:θ 12224:⁡ 12169:− 12047:θ 12043:⁡ 12018:θ 12014:⁡ 11990:θ 11986:⁡ 11970:− 11961:θ 11957:⁡ 11863:θ 11859:⁡ 11834:θ 11830:⁡ 11806:θ 11802:⁡ 11786:− 11777:θ 11773:⁡ 11625:/2 11208:− 11100:θ 11096:⁡ 11071:θ 11067:⁡ 11043:θ 11039:⁡ 10957:θ 10953:⁡ 10928:θ 10924:⁡ 10900:θ 10896:⁡ 10880:− 10871:θ 10867:⁡ 10697:θ 10693:⁡ 10663:θ 10659:⁡ 10643:− 10634:θ 10630:⁡ 10466:θ 10462:⁡ 10433:θ 10429:⁡ 10413:− 10404:θ 10400:⁡ 10313:⋅ 10240:⋅ 10167:⋅ 9922:⋅ 9860:⋅ 9798:⋅ 9599:, we have 9414:− 9306:θ 9302:⁡ 9277:θ 9273:⁡ 9249:θ 9245:⁡ 9163:θ 9159:⁡ 9134:θ 9130:⁡ 9106:θ 9102:⁡ 9086:− 9077:θ 9073:⁡ 8968:θ 8964:⁡ 8924:θ 8920:⁡ 8894:− 8885:θ 8881:⁡ 8713:θ 8709:⁡ 8680:θ 8676:⁡ 8660:− 8651:θ 8647:⁡ 8512:⋅ 8439:⋅ 8366:⋅ 8143:⋅ 8081:⋅ 7978:⋅ 7925:) of its 7825:θ 7821:⁡ 7792:⋅ 7769:⋅ 7746:⋅ 7703:At 7652:θ 7648:⁡ 7620:θ 7616:⁡ 7580:⋅ 7551:θ 7547:⁡ 7538:− 7529:θ 7525:⁡ 7489:⋅ 7460:θ 7456:⁡ 7438:θ 7434:⁡ 7398:⋅ 7329:θ 7325:⁡ 7294:θ 7290:⁡ 7243:θ 7239:⁡ 7219:θ 7215:⁡ 7156:θ 7152:⁡ 7141:− 7132:θ 7128:⁡ 7069:θ 7065:⁡ 7045:θ 7041:⁡ 6933:reference 6896:reflected 6823:(in bold 6589:ϵ 6525:ϵ 6510:μ 6454:Ω 6447:≈ 6435:ϵ 6420:μ 6380:ϵ 6372:μ 6353:impedance 6319:ϵ 6272:ϵ 6262:μ 6220:ϵ 6210:μ 6158:ϵ 6155:μ 6069:μ 6061:ϵ 5986:ϵ 5983:μ 5899:ϵ 5873:μ 5791:× 5783:− 5768:ϵ 5765:ω 5753:× 5733:μ 5730:ω 5613:× 5605:− 5590:ω 5578:× 5558:ω 5501:⋅ 5413:ω 5311:ω 5246:. 5127:real part 5023:ω 5020:− 5013:⋅ 4950:intrinsic 4686:μ 4662:ϵ 4608:isotropic 4470:in 1875. 4395:In 1808, 4340:interfere 4276:θ 4263:θ 4256:⁡ 4239:θ 4235:− 4226:θ 4219:⁡ 4151:θ 4138:θ 4131:⁡ 4114:θ 4110:− 4101:θ 4094:⁡ 4085:− 4007:θ 4003:⁡ 3986:θ 3982:⁡ 3879:is zero, 3774:θ 3770:⁡ 3746:θ 3742:⁡ 3644:: 3540:θ 3536:⁡ 3511:θ 3507:⁡ 3483:θ 3479:⁡ 3424:θ 3420:⁡ 3395:θ 3391:⁡ 3367:θ 3363:⁡ 3347:− 3338:θ 3334:⁡ 3282:θ 3278:⁡ 3253:θ 3249:⁡ 3225:θ 3221:⁡ 3166:θ 3162:⁡ 3137:θ 3133:⁡ 3109:θ 3105:⁡ 3089:− 3080:θ 3076:⁡ 2996:θ 2965:θ 2950:θ 2919:θ 2356:− 2183:effective 2099:− 2049:− 1956:θ 1952:⁡ 1912:θ 1908:⁡ 1872:− 1844:θ 1840:⁡ 1824:− 1800:θ 1796:⁡ 1760:− 1710:θ 1706:⁡ 1679:θ 1675:⁡ 1649:θ 1645:⁡ 1629:− 1618:θ 1614:⁡ 1521:θ 1517:⁡ 1481:− 1452:θ 1448:⁡ 1409:θ 1405:⁡ 1369:− 1351:− 1340:θ 1336:⁡ 1288:θ 1284:⁡ 1257:θ 1253:⁡ 1227:θ 1223:⁡ 1207:− 1196:θ 1192:⁡ 966:θ 962:⁡ 935:θ 931:⁡ 905:θ 901:⁡ 885:− 874:θ 870:⁡ 786:θ 782:⁡ 755:θ 751:⁡ 725:θ 721:⁡ 705:− 694:θ 690:⁡ 637:following 518:θ 514:⁡ 487:θ 483:⁡ 435:θ 420:θ 358:at point 227:isotropic 208:reflected 116:physicist 16915:Thinfilm 16712:, 1910, 16691:295–413. 16387:719–29 ( 16195:141–63, 16166:105, pp. 15983:Archived 15880:positive 15724:See also 15718:parallel 15572:becomes 13569:), and ( 11631:which is 11548:are due 11536:, where 11456:) with ( 10056: , 9984: , 9977: , 9694: , 9673:For the 8259: , 8231: , 8224: , 7872:For the 6926:redefine 6924:, if we 6860:towards 6713:, 6040:, where 5840: , 5833: , 5542:and the 5342: 5213:argument 5210:negative 5141:; hence 4940:uniform 4783:relative 4755:relative 4626:,  4622:,  4618:,  4508:circular 4493:argument 2853:negative 2849:magnetic 1020:are the 216:magnetic 173:Overview 16955:Physics 16702: 16689: 16627: 16617: 16564:Sources 16547:187–97. 16545: 16541:‍ 16537: 16495:Bibcode 16464:‍ 16454:13–50, 16452: 16448: 16433:589–90. 16431: 16427: 16423: 16419: 16406: 16389:extrait 16385: 16381: 16367: 16354: 16352:760–61, 16350: 16339:781–96. 16337: 16333: 16329: 16325: 16303: 16299: 16286: 16282: 16278: 16263:, 2021. 16252:4058004 16249:: 16233:17, pp. 16214: 16210: 16193: 16189: 16183:1817), 16181:‍ 16168: 16164: 16143: 16114:‍ 16020: 16007: 15874:‍ 15846:‍ 15822: 15710:Neumann 15680:‍ 15675:‍ 15664: 15660: 15655: 15645: 15613:) and ( 15568:, then 15550:) and ( 15445:‍ 15435: 15430:‍ 15426:‍ 15416: 15411:‍ 15403: 15398: 15388: 15384: 15379:‍ 15370: 15366:‍ 15356: 15347: 15343:‍ 15333:‍ 15322:‍ 15313: 15308:‍ 15304:‍ 15294: 15289:‍ 15284:‍ 15275: 15270:‍ 15266:‍ 15256: 15251:‍ 13543:‍ 13532: 13522: 13514:) and ( 12602:‍ 12585:) and ( 12138:‍ 12100: 12096: 11714:) and ( 11696: 11645: 11633:‍ 11629:‍ 11610:), the 11529: 11525: 11518:‍ 11515:⁠ 11503:⁠ 11499:‍ 11475:grazing 11462:) and ( 11450:) and ( 11430: 11426: 11414: 11412:, hence 11409:‍ 11399: 11394: 11388: 11163: 11156: 11146:‍ 10822:‍ 10598:) and ( 10098:‍ 10093: 10089: 10083: 10079: 10071: 10067:‍ 10058: 10047: 9993: 9986: 9979: 9971: 9963:If the 9717: 9709: 9705:‍ 9696: 9685: 9657: 9647: 9643: 9638: 9634: 9624: 9622:, hence 9619:‍ 9615: 9606: 9601: 9595: 9584:‍ 9369: 9362: 9352:‍ 9028:‍ 8297:‍ 8286: 8282: 8274: 8270:‍ 8261: 8250: 8240: 8233: 8226: 8218: 7911: 7697:Hence: 6972:‍ 6963:‍ 6945:‍ 6941: 6875: 6797: 6787: 6777:‍ 6772: 6768: 6761:‍ 6757: 6747: 6737:‍ 6728:‍ 6719:‍ 6683: 6670:‍ 6658:‍ 6548: 6471:‍ 6339:⁠ 6302:⁠ 6243: 6180:‍ 6176: 6118:‍ 6037:‍ 6032: 6028: 6022: 5851:form a 5849: 5842: 5835: 5692:‍ 5687:‍ 5678: 5674: 5667: 5663: 5653: 5649: 5642: 5640:Putting 5355:‍ 5302:‍ 5285: 5276:‍ 5265: 5232: 5223:‍ 5206:advance 5178: 5115:is the 5105:is the 5087:is the 5077:is the 4636:related 4632: 4612:‍ 4525:History 4523: 4385:History 4319:‍ 4189:‍ 4061:‍ 4052: 4048: 4045:⁠ 4028:⁠ 3945:‍ 3846:⁠ 3824:⁠ 3612:⁠ 3590:⁠ 2167: 1137:is the 276:to the 198:, both 16941:Portal 16884: 16857: 16834: 16815: 16796: 16740:This " 16672: 16657: 16651:Optics 16642: 16636:Optics 16608: 16586: 16539:6, no. 16535:, vol. 16513: 16466:(2.2). 16446:, vol. 16421:737–9, 16369:177–9. 16331:393–4, 16305:133–5. 16247:Zenodo 16243: 16239: 16235: 16231: 16229:, vol. 16216:646–8. 16187:, vol. 16162:, vol. 16145:191–2. 15950: 15698:normal 15586:) to ( 15556:), if 15473:arctan 13810:) to ( 13798:) to ( 13733: 13730: 13727: 13721: 13718: 13599:) by ( 13575:) to ( 13468:where 11470:normal 11390:→ 90°) 10551: 10548: 10540: 10537: 10534: 10526: 10523: 9597:→ 90°) 8801:) to ( 8754: 8751: 8743: 8740: 8737: 8729: 8726: 7730: 7727: 7724: 7368:) are 6969:< 0 6734:< 0 6673:, and 6550:For a 6296:For a 6110:From ( 5938:where 5462:phasor 5391:gives 5062:where 4964:, the 4818:. For 4711:where 4600:linear 4558:, and 4460:normal 4445:purely 4417:reason 4370:, and 2004:using 1146:= 1, 2 1128:where 1002:where 378:normal 298:normal 273:normal 16976:Light 16511:S2CID 15792:Notes 15287:, and 10027:other 5155:phase 4942:plane 4349:laser 4315:limit 2770:phase 2596:= 45° 2581:= 1.5 2529:> 2505:= 1.5 2430:≈ 1.5 621:, or 601:, or 589:power 557:power 553:below 312:below 280:(the 112:media 104:light 16882:ISBN 16855:ISBN 16832:ISBN 16813:ISBN 16794:ISBN 16700:vol. 16670:ISBN 16655:ISBN 16640:ISBN 16625:vol. 16606:ISBN 16584:ISBN 16116:213. 15948:ISBN 15854:for 15708:and 15628:and 15243:are 15234:and 13661:for 13563:), ( 13557:), ( 13551:), ( 12577:real 11604:and 11594:and 11584:and 11574:and 11558:and 11550:only 11542:and 11485:The 11423:→ −1 11274:and 10994:and 10813:and 10360:and 10011:the 9728:and 9665:The 9480:and 9200:and 9019:and 8563:and 7903:and 7864:The 6894:for 6833:and 6817:and 6770:> 5952:and 5942:and 5822:and 5712:and 5700:and 4908:and 4898:and 4744:and 4717:and 4634:are 4602:and 4535:and 4482:and 4377:The 4309:and 3920:and 3907:and 3851:cos( 3704:the 3587:and 2885:and 2877:and 2867:and 2787:and 2739:and 2711:and 2693:and 2672:and 2497:and 2177:and 2073:and 2008:and 1141:and 1061:and 1011:and 617:(or 597:(or 458:and 398:and 349:and 202:and 165:and 106:(or 98:(or 94:The 16503:doi 16456:doi 16276:pp. 16257:doi 15940:doi 15673:= 0 15657:= 0 15433:sin 15428:for 15414:cos 15400:= 0 15368:sin 15345:sin 15311:cos 15306:for 15292:sin 15273:cos 15268:for 15254:sin 15149:cos 15120:cos 15092:cos 15063:cos 14968:cos 14939:cos 14911:cos 14882:cos 14395:cos 14366:cos 14338:cos 14255:cos 14226:cos 14198:cos 14169:cos 14088:cos 14059:cos 14031:cos 13948:cos 13919:cos 13891:cos 13862:cos 13281:cos 13252:cos 13219:cos 13203:cos 13155:cos 13137:cos 13076:cos 13047:cos 13019:cos 12918:cos 12889:cos 12856:cos 12840:cos 12792:cos 12774:cos 12713:cos 12684:cos 12656:cos 12563:26T 12518:cos 12489:cos 12453:cos 12437:cos 12347:25T 12302:cos 12273:cos 12237:cos 12221:cos 12098:cos 12040:cos 12011:cos 11983:cos 11954:cos 11856:cos 11827:cos 11799:cos 11770:cos 11671:or 11520:Re{ 11473:at 11439:→ 0 11428:and 11407:→ 0 11397:cos 11373:At 11158:= θ 11141:At 11093:cos 11064:cos 11036:cos 10950:cos 10921:cos 10893:cos 10864:cos 10690:cos 10656:cos 10627:cos 10459:cos 10426:cos 10397:cos 9659:→ 0 9645:and 9617:→ 0 9604:cos 9579:At 9364:= θ 9347:At 9299:cos 9270:cos 9242:cos 9156:cos 9127:cos 9099:cos 9070:cos 8961:cos 8917:cos 8878:cos 8706:cos 8673:cos 8644:cos 7818:sin 7645:cos 7613:sin 7544:cos 7522:sin 7453:cos 7431:sin 7322:cos 7287:sin 7236:cos 7212:sin 7149:cos 7125:sin 7062:cos 7038:sin 6898:). 6593:rel 6529:rel 6514:rel 6450:377 6355:is 6323:rel 6276:rel 6266:rel 5665:and 5249:If 5243:−iω 5187:by 5167:by 5099:), 4918:to 4841:rel 4835:), 4828:rel 4816:= 1 4814:rel 4791:rel 4767:rel 4638:by 4582:). 4528:). 4401:one 4328:→ 0 4253:tan 4216:tan 4128:sin 4091:sin 4050:sin 4000:sin 3979:sin 3898:of 3892:= 0 3866:= 1 3767:cos 3739:cos 3627:+ 1 3585:+ 1 3533:cos 3504:cos 3476:cos 3417:cos 3388:cos 3360:cos 3331:cos 3275:cos 3246:cos 3218:cos 3159:cos 3130:cos 3102:cos 3073:cos 2899:or 2568:≤ 1 2556:= 1 2495:= 1 2465:to 2440:= 1 2315:= 0 1949:cos 1905:sin 1837:cos 1793:sin 1703:cos 1672:cos 1642:cos 1611:cos 1514:sin 1445:cos 1402:sin 1333:cos 1281:cos 1250:cos 1220:cos 1189:cos 959:cos 928:cos 898:cos 867:cos 826:is 779:cos 748:cos 718:cos 687:cos 646:is 511:sin 480:sin 308:= 0 72:At 16967:: 16870:, 16683:, 16531:, 16509:. 16501:. 16491:40 16489:. 16268:^ 16255:/ 16158:, 15998:^ 15971:^ 15946:. 15938:. 15886:jω 15851:−i 15640:39 15616:31 15610:29 15589:38 15583:29 15526:39 15358:− 15328:31 15217:. 15198:38 15013:37 14829:36 14757:p0 14733:35 14655:p0 14631:34 14563:s0 14539:33 14461:s0 14434:32 14290:31 14124:30 13983:29 13818:cμ 13813:26 13807:21 13801:16 13795:13 13585:. 13578:28 13572:25 13566:22 13560:21 13554:14 13548:13 13534:= 13500:. 13326:28 12963:27 12588:22 12582:14 12410:Re 12194:Re 12085:26 11901:25 11717:21 11711:13 11705:. 11694:2Z 11682:/2 11680:EH 11663:xy 11641:2Z 11623:EH 11596:-z 11592:xy 11576:xy 11465:16 11459:15 11453:24 11447:23 11441:. 11364:24 11292:p0 11265:23 11187:p0 11167:0) 11132:22 10985:21 10795:20 10601:18 10595:17 10583:19 10544:at 10345:18 10101:, 10095:YE 10042:−z 10004:−z 9954:17 9661:. 9640:−1 9570:16 9498:s0 9471:15 9393:s0 9373:0) 9338:14 9191:13 9001:12 8804:10 8786:11 8747:at 8544:10 8300:, 8294:YE 8292:= 6905:, 6842:xy 6802:xz 6660:, 6341:. 6107:. 6034:YE 5718:: 5193:− 5191:ωt 5184:ωt 5172:+ 5170:ωt 5164:ωt 5150:. 5119:, 5109:, 5081:, 4935:. 4857:. 4849:≈ 4805:. 4793:= 4769:= 4761:) 4552:, 4543:. 4366:, 4351:. 4330:. 4317:as 3928:. 3868:. 3620:= 3578:= 2616:: 2549:= 2308:= 2300:, 2012:. 1070:: 1042:= 1035:= 633:at 625:) 605:) 462:: 411:: 389:, 373:OT 367:OR 337:IO 294:xy 290:in 286:in 134:eɪ 16943:: 16923:. 16863:. 16840:. 16821:. 16802:. 16773:) 16767:( 16762:) 16758:( 16748:. 16706:. 16704:2 16676:. 16661:. 16646:. 16631:. 16612:. 16590:. 16517:. 16505:: 16497:: 16458:: 16259:: 16199:. 15993:. 15956:. 15942:: 15892:e 15884:+ 15872:e 15860:. 15857:j 15837:i 15831:j 15826:; 15824:e 15819:k 15817:E 15807:1 15678:, 15671:p 15668:r 15652:s 15649:r 15634:p 15631:r 15625:s 15622:r 15604:2 15601:n 15598:1 15595:n 15578:n 15570:Y 15565:μ 15559:ϵ 15553:5 15547:4 15544:( 15528:) 15524:( 15507:) 15502:1 15498:n 15493:/ 15487:2 15483:n 15479:( 15470:= 15465:i 15441:t 15438:θ 15422:i 15419:θ 15395:p 15392:r 15382:, 15376:i 15373:θ 15363:1 15360:n 15353:t 15350:θ 15340:2 15337:n 15319:t 15316:θ 15300:i 15297:θ 15281:i 15278:θ 15262:t 15259:θ 15240:t 15237:θ 15231:i 15228:θ 15214:R 15210:T 15200:) 15196:( 15179:. 15173:2 15168:| 15160:t 15144:1 15140:n 15136:+ 15131:i 15115:2 15111:n 15103:t 15087:1 15083:n 15074:i 15058:2 15054:n 15047:| 15042:= 15037:p 15033:R 15015:) 15011:( 14992:2 14987:| 14979:t 14963:2 14959:n 14955:+ 14950:i 14934:1 14930:n 14922:t 14906:2 14902:n 14893:i 14877:1 14873:n 14866:| 14861:= 14856:s 14852:R 14831:) 14827:( 14810:. 14801:1 14797:n 14793:+ 14788:2 14784:n 14776:1 14772:n 14768:2 14762:= 14753:t 14735:) 14731:( 14709:1 14705:n 14701:+ 14696:2 14692:n 14684:1 14680:n 14671:2 14667:n 14660:= 14651:r 14633:) 14629:( 14607:2 14603:n 14599:+ 14594:1 14590:n 14582:1 14578:n 14574:2 14568:= 14559:t 14541:) 14537:( 14515:2 14511:n 14507:+ 14502:1 14498:n 14490:2 14486:n 14477:1 14473:n 14466:= 14457:r 14436:) 14432:( 14415:. 14406:t 14390:1 14386:n 14382:+ 14377:i 14361:2 14357:n 14349:i 14333:1 14329:n 14325:2 14319:= 14314:p 14310:t 14292:) 14288:( 14266:t 14250:1 14246:n 14242:+ 14237:i 14221:2 14217:n 14209:t 14193:1 14189:n 14180:i 14164:2 14160:n 14153:= 14148:p 14144:r 14126:) 14122:( 14099:t 14083:2 14079:n 14075:+ 14070:i 14054:1 14050:n 14042:i 14026:1 14022:n 14018:2 14012:= 14007:s 14003:t 13985:) 13981:( 13959:t 13943:2 13939:n 13935:+ 13930:i 13914:1 13910:n 13902:t 13886:2 13882:n 13873:i 13857:1 13853:n 13846:= 13841:s 13837:r 13821:0 13780:; 13771:0 13763:c 13756:2 13752:n 13746:= 13741:2 13737:Y 13724:; 13710:0 13702:c 13695:1 13691:n 13685:= 13680:1 13676:Y 13664:μ 13658:0 13655:μ 13637:. 13626:c 13621:n 13616:= 13613:Y 13602:5 13596:4 13539:i 13536:θ 13529:t 13526:θ 13517:5 13511:4 13488:1 13485:= 13482:T 13479:+ 13476:R 13456:) 13451:p 13447:R 13443:+ 13438:s 13434:R 13430:( 13425:2 13422:1 13417:= 13414:R 13395:) 13390:p 13386:T 13382:+ 13377:s 13373:T 13369:( 13364:2 13361:1 13356:= 13353:T 13338:T 13328:) 13324:( 13303:2 13298:) 13292:t 13276:1 13272:Y 13268:+ 13263:i 13247:2 13243:Y 13238:( 13230:t 13214:i 13198:2 13194:Y 13188:1 13184:Y 13180:4 13174:= 13166:i 13148:t 13126:1 13122:Y 13114:2 13110:Y 13100:2 13095:) 13087:t 13071:1 13067:Y 13063:+ 13058:i 13042:2 13038:Y 13030:i 13014:1 13010:Y 13006:2 13000:( 12995:= 12990:p 12986:T 12965:) 12961:( 12940:2 12935:) 12929:t 12913:2 12909:Y 12905:+ 12900:i 12884:1 12880:Y 12875:( 12867:t 12851:i 12835:2 12831:Y 12825:1 12821:Y 12817:4 12811:= 12803:i 12785:t 12763:1 12759:Y 12751:2 12747:Y 12737:2 12732:) 12724:t 12708:2 12704:Y 12700:+ 12695:i 12679:1 12675:Y 12667:i 12651:1 12647:Y 12643:2 12637:( 12632:= 12627:s 12623:T 12607:Z 12599:θ 12593:y 12565:) 12561:( 12540:2 12535:| 12529:t 12513:1 12509:Y 12505:+ 12500:i 12484:2 12480:Y 12475:| 12469:} 12464:t 12448:i 12432:2 12428:Y 12422:1 12418:Y 12414:{ 12405:4 12398:= 12393:p 12389:R 12382:1 12379:= 12374:p 12370:T 12349:) 12345:( 12324:2 12319:| 12313:t 12297:2 12293:Y 12289:+ 12284:i 12268:1 12264:Y 12259:| 12253:} 12248:t 12232:i 12216:2 12212:Y 12206:1 12202:Y 12198:{ 12189:4 12182:= 12177:s 12173:R 12166:1 12163:= 12158:s 12154:T 12133:T 12129:R 12124:y 12103:θ 12087:) 12083:( 12064:2 12059:| 12051:t 12035:1 12031:Y 12027:+ 12022:i 12006:2 12002:Y 11994:t 11978:1 11974:Y 11965:i 11949:2 11945:Y 11938:| 11933:= 11928:p 11924:R 11903:) 11899:( 11880:2 11875:| 11867:t 11851:2 11847:Y 11843:+ 11838:i 11822:1 11818:Y 11810:t 11794:2 11790:Y 11781:i 11765:1 11761:Y 11754:| 11749:= 11744:s 11740:R 11702:θ 11698:) 11692:/ 11690:E 11687:( 11674:E 11668:H 11659:x 11654:Y 11650:Z 11639:/ 11637:E 11627:, 11617:k 11607:H 11601:E 11587:H 11581:E 11572:z 11567:k 11561:H 11555:E 11545:H 11539:E 11534:} 11532:H 11527:× 11522:E 11512:2 11509:/ 11506:1 11437:p 11434:t 11421:p 11418:r 11405:i 11402:θ 11385:i 11382:θ 11380:( 11366:) 11362:( 11345:. 11336:1 11332:Y 11328:+ 11323:2 11319:Y 11311:1 11307:Y 11303:2 11297:= 11288:t 11267:) 11263:( 11241:1 11237:Y 11233:+ 11228:2 11224:Y 11216:1 11212:Y 11203:2 11199:Y 11192:= 11183:r 11165:= 11160:t 11153:i 11151:θ 11149:( 11134:) 11130:( 11113:. 11104:t 11088:1 11084:Y 11080:+ 11075:i 11059:2 11055:Y 11047:i 11031:1 11027:Y 11023:2 11017:= 11012:p 11008:t 10987:) 10983:( 10961:t 10945:1 10941:Y 10937:+ 10932:i 10916:2 10912:Y 10904:t 10888:1 10884:Y 10875:i 10859:2 10855:Y 10848:= 10843:p 10839:r 10819:p 10816:t 10810:p 10807:r 10797:) 10793:( 10772:. 10766:p 10762:t 10756:2 10752:Y 10747:= 10738:p 10734:r 10728:1 10724:Y 10720:+ 10715:1 10711:Y 10701:t 10685:p 10681:t 10676:= 10667:i 10651:p 10647:r 10638:i 10607:7 10585:) 10581:( 10564:. 10560:0 10557:= 10554:y 10530:} 10514:t 10510:H 10506:= 10497:r 10493:H 10489:+ 10484:i 10480:H 10470:t 10454:t 10450:E 10446:= 10437:i 10421:r 10417:E 10408:i 10392:i 10388:E 10363:H 10357:E 10347:) 10343:( 10322:. 10316:r 10307:t 10302:k 10297:i 10293:e 10286:p 10282:t 10276:2 10272:Y 10267:= 10258:t 10254:H 10243:r 10234:r 10229:k 10224:i 10220:e 10213:p 10209:r 10203:1 10199:Y 10194:= 10185:r 10181:H 10170:r 10161:i 10156:k 10151:i 10147:e 10141:1 10137:Y 10132:= 10123:i 10119:H 10091:= 10087:H 10077:t 10074:H 10069:, 10064:r 10061:H 10054:i 10051:H 10036:H 10023:) 10019:p 10014:H 10009:( 9998:H 9989:H 9982:E 9975:k 9966:E 9956:) 9952:( 9931:. 9925:r 9916:t 9911:k 9906:i 9902:e 9895:p 9891:t 9887:= 9878:t 9874:E 9863:r 9854:r 9849:k 9844:i 9840:e 9833:p 9829:r 9825:= 9816:r 9812:E 9801:r 9792:i 9787:k 9782:i 9778:e 9774:= 9765:i 9761:E 9740:E 9734:p 9731:t 9725:p 9722:r 9715:t 9712:E 9707:, 9702:r 9699:E 9692:i 9689:E 9680:E 9675:p 9667:p 9654:s 9651:t 9636:→ 9631:s 9628:r 9612:i 9609:θ 9592:i 9589:θ 9587:( 9572:) 9568:( 9551:. 9542:2 9538:Y 9534:+ 9529:1 9525:Y 9517:1 9513:Y 9509:2 9503:= 9494:t 9473:) 9469:( 9447:2 9443:Y 9439:+ 9434:1 9430:Y 9422:2 9418:Y 9409:1 9405:Y 9398:= 9389:r 9371:= 9366:t 9359:i 9357:θ 9355:( 9340:) 9336:( 9319:. 9310:t 9294:2 9290:Y 9286:+ 9281:i 9265:1 9261:Y 9253:i 9237:1 9233:Y 9229:2 9223:= 9218:s 9214:t 9193:) 9189:( 9167:t 9151:2 9147:Y 9143:+ 9138:i 9122:1 9118:Y 9110:t 9094:2 9090:Y 9081:i 9065:1 9061:Y 9054:= 9049:s 9045:r 9025:s 9022:t 9016:s 9013:r 9003:) 8999:( 8978:, 8972:t 8956:s 8952:t 8946:2 8942:Y 8937:= 8928:i 8912:s 8908:r 8902:1 8898:Y 8889:i 8873:1 8869:Y 8859:s 8855:t 8850:= 8841:s 8837:r 8833:+ 8830:1 8810:7 8798:8 8788:) 8784:( 8767:. 8763:0 8760:= 8757:y 8733:} 8717:t 8701:t 8697:H 8693:= 8684:i 8668:r 8664:H 8655:i 8639:i 8635:H 8625:t 8621:E 8617:= 8608:r 8604:E 8600:+ 8595:i 8591:E 8566:H 8560:E 8546:) 8542:( 8521:. 8515:r 8506:t 8501:k 8496:i 8492:e 8485:s 8481:t 8475:2 8471:Y 8466:= 8457:t 8453:H 8442:r 8433:r 8428:k 8423:i 8419:e 8412:s 8408:r 8402:1 8398:Y 8393:= 8384:r 8380:H 8369:r 8360:i 8355:k 8350:i 8346:e 8340:1 8336:Y 8331:= 8322:i 8318:H 8290:H 8280:t 8277:H 8272:, 8267:r 8264:H 8257:i 8254:H 8245:H 8236:H 8229:E 8222:k 8213:H 8207:z 8201:E 8195:E 8190:s 8177:) 8175:9 8173:( 8152:. 8146:r 8137:t 8132:k 8127:i 8123:e 8116:s 8112:t 8108:= 8099:t 8095:E 8084:r 8075:r 8070:k 8065:i 8061:e 8054:s 8050:r 8046:= 8037:r 8033:E 8008:) 8006:8 8004:( 7987:, 7981:r 7972:i 7967:k 7962:i 7958:e 7954:= 7949:i 7945:E 7928:z 7922:3 7916:E 7909:s 7906:t 7900:s 7897:r 7891:z 7885:z 7879:E 7874:s 7866:s 7856:) 7854:7 7852:( 7835:. 7829:i 7815:x 7812:k 7807:1 7803:n 7799:= 7795:r 7786:t 7781:k 7776:= 7772:r 7763:r 7758:k 7753:= 7749:r 7740:i 7735:k 7721:, 7717:0 7714:= 7711:y 7690:) 7688:6 7686:( 7665:. 7661:) 7656:t 7642:y 7637:2 7633:n 7629:+ 7624:i 7610:x 7605:1 7601:n 7597:( 7594:k 7591:= 7583:r 7574:t 7569:k 7560:) 7555:i 7541:y 7533:i 7519:x 7516:( 7513:k 7508:1 7504:n 7500:= 7492:r 7483:r 7478:k 7469:) 7464:i 7450:y 7447:+ 7442:i 7428:x 7425:( 7422:k 7417:1 7413:n 7409:= 7401:r 7392:i 7387:k 7365:3 7342:, 7338:) 7333:t 7317:2 7313:n 7307:j 7303:+ 7298:i 7282:1 7278:n 7272:i 7268:( 7265:k 7262:= 7252:) 7247:t 7232:j 7228:+ 7223:t 7208:i 7204:( 7201:k 7196:2 7192:n 7188:= 7179:t 7174:k 7165:) 7160:i 7145:j 7136:i 7121:i 7117:( 7114:k 7109:1 7105:n 7101:= 7092:r 7087:k 7078:) 7073:i 7058:j 7054:+ 7049:i 7034:i 7030:( 7027:k 7022:1 7018:n 7014:= 7005:i 7000:k 6983:k 6980:2 6977:n 6967:y 6958:k 6955:1 6952:n 6947:1 6943:= 6938:n 6929:k 6921:ω 6912:2 6907:ω 6891:r 6881:t 6872:t 6869:θ 6863:i 6857:j 6851:i 6848:θ 6836:y 6830:x 6820:j 6814:i 6808:y 6795:2 6792:Y 6785:2 6782:n 6774:0 6765:y 6755:1 6752:Y 6745:1 6742:n 6732:y 6724:) 6722:z 6717:, 6715:y 6711:x 6709:( 6700:2 6697:n 6691:1 6688:n 6680:t 6676:k 6666:r 6662:k 6654:i 6650:k 6634:) 6621:. 6618:n 6614:/ 6608:0 6604:Z 6600:= 6580:/ 6573:0 6569:Z 6565:= 6562:Z 6545:. 6520:/ 6504:= 6499:0 6495:Z 6490:/ 6486:Z 6458:, 6439:0 6430:/ 6424:0 6414:= 6409:0 6405:Z 6394:. 6376:/ 6367:= 6364:Z 6348:5 6343:( 6313:= 6310:n 6284:. 6256:= 6253:n 6240:. 6224:0 6214:0 6201:/ 6196:1 6193:= 6190:c 6173:. 6147:/ 6142:1 6139:= 6136:n 6132:/ 6128:c 6113:4 6096:) 6094:5 6092:( 6075:. 6065:/ 6056:= 6053:Y 6030:= 6026:H 6013:) 6011:4 6009:( 5992:. 5977:c 5974:= 5971:n 5955:E 5949:H 5944:E 5940:H 5922:, 5918:H 5915:n 5912:= 5905:E 5902:c 5892:E 5889:n 5886:= 5879:H 5876:c 5858:2 5845:H 5838:E 5831:k 5825:μ 5819:ϵ 5800:. 5795:H 5787:k 5780:= 5772:E 5757:E 5749:k 5745:= 5737:H 5715:H 5709:E 5703:D 5697:B 5690:, 5684:E 5681:ϵ 5676:= 5671:D 5659:H 5656:μ 5651:= 5646:B 5622:. 5617:H 5609:k 5602:= 5594:D 5582:E 5574:k 5570:= 5562:B 5531:) 5529:3 5527:( 5510:. 5504:r 5498:k 5494:i 5490:e 5483:k 5479:E 5456:e 5446:) 5444:2 5442:( 5425:. 5421:c 5417:/ 5410:n 5407:= 5404:k 5389:k 5385:. 5373:n 5369:/ 5365:c 5351:) 5349:p 5346:v 5344:( 5323:, 5319:k 5315:/ 5298:ℓ 5293:e 5287:e 5282:k 5280:E 5271:1 5262:k 5256:r 5251:ℓ 5237:e 5234:e 5229:k 5227:E 5218:1 5201:e 5195:ϕ 5189:− 5182:− 5174:ϕ 5159:ϕ 5144:k 5138:k 5132:r 5122:t 5112:ω 5102:r 5093:k 5084:k 5074:i 5067:k 5065:E 5055:) 5053:1 5051:( 5034:, 5029:) 5026:t 5016:r 5010:k 5006:( 5003:i 4999:e 4992:k 4988:E 4970:E 4933:Z 4929:Y 4921:n 4916:Z 4911:μ 4905:ϵ 4900:Z 4895:n 4889:H 4883:E 4878:Z 4871:c 4866:n 4854:0 4851:μ 4847:μ 4838:μ 4825:μ 4811:μ 4802:0 4799:μ 4797:/ 4795:μ 4788:μ 4778:0 4775:ϵ 4773:/ 4771:ϵ 4764:ϵ 4750:0 4747:μ 4741:0 4738:ϵ 4720:μ 4714:ϵ 4695:, 4690:H 4683:= 4675:B 4666:E 4659:= 4651:D 4628:H 4624:D 4620:B 4616:E 4510:. 4488:p 4485:r 4479:s 4476:r 4326:i 4323:θ 4291:. 4285:) 4280:t 4272:+ 4267:i 4259:( 4248:) 4243:t 4230:i 4222:( 4210:= 4205:p 4201:r 4186:p 4183:r 4166:. 4160:) 4155:t 4147:+ 4142:i 4134:( 4123:) 4118:t 4105:i 4097:( 4082:= 4077:s 4073:r 4058:t 4055:θ 4041:1 4038:n 4034:/ 4031:1 4011:t 3996:/ 3990:i 3974:1 3970:n 3966:= 3961:2 3957:n 3942:s 3939:r 3922:p 3918:s 3913:s 3910:r 3904:p 3901:r 3890:T 3881:t 3877:T 3864:T 3855:) 3853:θ 3842:1 3839:n 3835:/ 3831:2 3828:n 3818:t 3801:2 3796:| 3791:t 3787:| 3778:i 3762:1 3758:n 3750:t 3734:2 3730:n 3723:= 3720:T 3694:T 3678:. 3673:2 3668:| 3663:r 3659:| 3655:= 3652:R 3641:r 3635:R 3625:p 3622:r 3618:p 3615:t 3608:1 3605:n 3601:/ 3597:2 3594:n 3583:s 3580:r 3576:s 3573:t 3552:. 3544:t 3528:1 3524:n 3520:+ 3515:i 3499:2 3495:n 3487:i 3471:1 3467:n 3463:2 3457:= 3448:p 3444:t 3436:, 3428:t 3412:1 3408:n 3404:+ 3399:i 3383:2 3379:n 3371:t 3355:1 3351:n 3342:i 3326:2 3322:n 3315:= 3306:p 3302:r 3294:, 3286:t 3270:2 3266:n 3262:+ 3257:i 3241:1 3237:n 3229:i 3213:1 3209:n 3205:2 3199:= 3190:s 3186:t 3178:, 3170:t 3154:2 3150:n 3146:+ 3141:i 3125:1 3121:n 3113:t 3097:2 3093:n 3084:i 3068:1 3064:n 3057:= 3048:s 3044:r 3020:n 3001:t 2970:i 2961:= 2955:r 2924:i 2901:p 2897:s 2892:r 2887:p 2883:s 2879:p 2875:s 2870:t 2864:r 2858:t 2844:r 2839:p 2834:r 2829:s 2805:0 2802:µ 2796:µ 2790:t 2784:r 2745:p 2742:R 2736:s 2733:R 2726:0 2723:R 2717:p 2714:R 2708:s 2705:R 2699:p 2696:R 2690:s 2687:R 2678:p 2675:R 2669:s 2666:R 2647:2 2642:s 2638:R 2634:= 2629:p 2625:R 2613:s 2610:R 2604:p 2601:R 2594:θ 2579:n 2573:θ 2566:θ 2554:p 2551:R 2547:s 2544:R 2534:2 2531:n 2527:1 2524:n 2503:2 2500:n 2493:1 2490:n 2480:p 2477:R 2471:2 2468:n 2462:1 2459:n 2438:1 2435:n 2428:2 2425:n 2408:. 2402:2 2397:| 2389:2 2385:n 2381:+ 2376:1 2372:n 2364:2 2360:n 2351:1 2347:n 2340:| 2335:= 2330:0 2326:R 2313:t 2310:θ 2306:i 2303:θ 2261:. 2257:) 2250:p 2245:R 2241:+ 2235:s 2230:R 2225:( 2219:2 2216:1 2211:= 2205:f 2202:f 2199:e 2194:R 2179:p 2175:s 2165:r 2162:θ 2158:i 2155:θ 2144:θ 2138:θ 2108:p 2103:R 2096:1 2093:= 2087:p 2082:T 2058:s 2053:R 2046:1 2043:= 2037:s 2032:T 2001:t 1998:θ 1981:. 1975:2 1970:| 1961:i 1944:2 1940:n 1936:+ 1929:2 1924:) 1917:i 1898:2 1894:n 1888:1 1884:n 1877:( 1869:1 1862:1 1858:n 1849:i 1832:2 1828:n 1817:2 1812:) 1805:i 1786:2 1782:n 1776:1 1772:n 1765:( 1757:1 1750:1 1746:n 1739:| 1734:= 1729:2 1724:| 1715:i 1698:2 1694:n 1690:+ 1684:t 1667:1 1663:n 1654:i 1637:2 1633:n 1623:t 1606:1 1602:n 1595:| 1590:= 1584:p 1579:R 1559:, 1553:2 1548:| 1538:2 1533:) 1526:i 1507:2 1503:n 1497:1 1493:n 1486:( 1478:1 1471:2 1467:n 1463:+ 1457:i 1440:1 1436:n 1426:2 1421:) 1414:i 1395:2 1391:n 1385:1 1381:n 1374:( 1366:1 1359:2 1355:n 1345:i 1328:1 1324:n 1317:| 1312:= 1307:2 1302:| 1293:t 1276:2 1272:n 1268:+ 1262:i 1245:1 1241:n 1232:t 1215:2 1211:n 1201:i 1184:1 1180:n 1173:| 1168:= 1162:s 1157:R 1144:i 1134:0 1131:Z 1116:, 1108:i 1104:n 1098:0 1094:Z 1088:= 1083:i 1079:Z 1067:2 1064:n 1058:1 1055:n 1048:0 1045:μ 1040:2 1037:μ 1033:1 1030:μ 1017:2 1014:Z 1008:1 1005:Z 990:, 985:2 980:| 971:i 954:1 950:Z 946:+ 940:t 923:2 919:Z 910:i 893:1 889:Z 879:t 862:2 858:Z 851:| 846:= 840:p 835:R 810:, 805:2 800:| 791:t 774:1 770:Z 766:+ 760:i 743:2 739:Z 730:t 713:1 709:Z 699:i 682:2 678:Z 671:| 666:= 660:s 655:R 628:T 608:R 529:. 523:t 506:2 502:n 498:= 492:i 475:1 471:n 446:, 440:r 431:= 425:i 404:t 401:θ 395:r 392:θ 386:i 383:θ 361:O 355:2 352:n 346:1 343:n 306:θ 282:z 195:2 192:n 186:1 183:n 167:p 163:s 149:/ 146:l 143:ɛ 140:n 137:ˈ 131:r 128:f 125:/ 121:( 86:s 78:s 38:. 20:)

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