573:(1690), was as follows. When a ray (meaning a narrow beam of light) passes through two similarly oriented calcite crystals at normal incidence, the ordinary ray emerging from the first crystal suffers only the ordinary refraction in the second, while the extraordinary ray emerging from the first suffers only the extraordinary refraction in the second. But when the second crystal is rotated 90° about the incident rays, the roles are interchanged, so that the ordinary ray emerging from the first crystal suffers only the extraordinary refraction in the second, and vice versa. At intermediate positions of the second crystal, each ray emerging from the first is doubly refracted by the second, giving four rays in total; and as the crystal is rotated from the initial orientation to the perpendicular one, the brightnesses of the rays vary, giving a smooth transition between the extreme cases in which there are only two final rays.
816:
1775:
31:
1763:
591:
373:
665:
218:
714:, he found that he could account for the partial reflection (including polarization by reflection) at the interface between two transparent isotropic media, provided that the vibrations of the aether were perpendicular to the plane of polarization. Thus the polarization, according to the received definition, was "in" a certain plane if the vibrations were
957:), there are three mutually perpendicular planes for which the speed of light is isotropic within the plane provided that the electric vectors are normal to the plane. This situation naturally draws attention to a plane normal to the vibrations as envisaged by Fresnel, and that plane is indeed the plane of polarization as defined by Fresnel or Malus.
735:
perpendicular to the plane of polarization, then the plane of polarization contained the wave-normal but not necessarily the ray. In his "Second Memoir" on double refraction, Fresnel formally adopted this new definition, acknowledging that it agreed with the old definition in an isotropic medium such as air, but not in a birefringent crystal.
842:
to the planes of vibration (as
Fresnel said), the planes of polarization will be crowded in the normal direction. To find the direction of the crowding, one could vary the polarization of the incident light in equal steps, and determine the planes of polarization of the diffracted light in the usual
769:
authors tend to identify with the "plane of polarization". We might therefore wish that
Fresnel had been less deferential to his predecessors. That scenario, however, is less realistic than it may seem, because even after Fresnel's transverse-wave theory was generally accepted, the direction of the
888:
vectors. Hence the electromagnetic theory would have reinforced the convention that the vibrations were normal to the plane of polarization — provided, of course, that one was familiar with the historical definition of the plane of polarization. But if one was influenced by physical considerations
734:
But he soon felt obliged to make a less radical change. In his successful model of double refraction, the displacement of the medium was constrained to be tangential to the wavefront, while the force was allowed to deviate from the displacement and from the wavefront. Hence, if the vibrations were
846:
In 1852, Stokes noted a much simpler experiment that leads to the same conclusion. Sunlight scattered from a patch of blue sky 90° from the sun is found, by the methods of Malus, to be polarized in the plane containing the line of sight and the sun. But it is obvious from the geometry that the
837:
is illuminated at normal incidence. At large angles of diffraction, the grating will appear somewhat edge-on, so that the directions of vibration will be crowded towards the direction parallel to the plane of the grating. If the planes of polarization coincide with the planes of vibration (as
939:
medium — that is, one in which the direction of polarization gradually rotates as the wave propagates — the choice of definition of the "plane of polarization" does not affect the existence or direction ("handedness") of the rotation. This is one context in which the ambiguity of the term
750:. Fresnel's definition remains compatible with the Merriam-Webster definition, which fails to specify the propagation direction. And it remains compatible with Stratton's definition, because that is given in the context of an isotropic medium, in which planes (2a) and (2b) merge into
608:
in 1811. In 1808, in the midst of confirming
Huygens' geometric description of double refraction (while disputing his physical explanation), Malus had discovered that when a ray of light is reflected off a non-metallic surface at the appropriate angle, it behaves like
850:
There was, however, a sense in which MacCullagh and
Neumann were correct. If we attempt an analogy between shear waves in a non-isotropic elastic solid, and EM waves in a magnetically isotropic but electrically non-isotropic crystal, the density must correspond to the magnetic
960:
In most contexts, however, the concept of a "plane of polarization" distinct from a plane containing the electric "vibrations" has arguably become redundant, and has certainly become a source of confusion. In the words of Born & Wolf, "it is… better not to use this term."
189:
Fresnel also admitted that, had he not felt constrained by the received terminology, it would have been more natural to define the plane of polarization as the plane containing the vibrations and the direction of propagation. That plane, which became known as the
871:
vibrations, because those have the greater propensity to interact with matter. In short, the MacCullagh-Neumann vibrations were the ones that had a mechanical analog, but
Fresnel's vibrations were the ones that were more likely to be detected in experiments.
494:
Whether by accident or by design, the plane of polarization has always been defined as the plane containing a field vector and a direction of propagation. In Fig. 1, there are three such planes, to which we may assign numbers for ease of reference:
1306:, Ser. 2, vol. 17, pp. 102–11 (May 1821), 167–96 (June 1821), 312–15 ("Postscript", July 1821); reprinted (with added section nos.) in H. de Sénarmont, E. Verdet, and L. Fresnel (eds.),
411:) vector and leaves the reader to presume that the "plane of polarization" contains that vector — and this interpretation indeed fits the examples he gives. The same vector is used to describe the polarization of radio signals and
782:. But it could not be extended to birefringent crystals — in which at least one refractive index varies with direction — because density is not directional. Hence his explanation of refraction required a directional variation in
368:
vectors, so that we tend to think of the direction of polarization as the direction of the electric vectors, and the "plane of polarization" as the plane containing the electric vectors and the direction of propagation.
727:
Adopting this hypothesis, it would have been more natural to have called the plane of polarisation that in which the oscillations are supposed to be made: but I wished to avoid making any change in the received
65:) and both propagation vectors, is sometimes called the "plane of polarization" by modern authors. Fresnel's "plane of polarization", traditionally used in optics, is the plane containing the magnetic vectors (
900:
However, it is not clear that a "plane of polarization" is needed at all: knowing what field vectors are involved, one can specify the polarization by specifying the orientation of a particular vector, or, as
310:) are in another direction, perpendicular to the first, and the direction of propagation is perpendicular to both the electric and the magnetic vectors. In this case the direction of propagation is both the
182:(1822 onward), found it more useful to choose the wave-normal direction, with the result that the supposed vibrations of the medium were then consistently perpendicular to the plane of polarization. In an
613:
of the two rays emerging from a calcite crystal. As this behavior had previously been known only in connection with double refraction, Malus described it in that context. In particular, he defined the
57:) and propagation directions (ray and wave-normal) for linearly-polarized plane electromagnetic waves in a non-magnetic birefringent crystal. The plane of vibration, containing both electric vectors (
543:
625:
and reflection — that is, the plane containing the incident ray, the normal to the reflective surface, and the polarized reflected ray. But, as we now know, this plane happens to contain the
998:(see e.g. Darrigol, 2012, pp. 253n, 257n); however, throughout this article, the existence of a stable plane of polarization requires the absence of optical rotation.
621:
refraction. This definition was all the more reasonable because it meant that when a ray was polarized by reflection (off an isotopic medium), the plane of polarization was the
648:", promptly adds: "In optics, however, the orientation of the vectors is specified traditionally by the 'plane of polarization,' by which is meant the plane normal to
553:
Printed label seen through a doubly-refracting calcite crystal and a modern polarizing filter (rotated to show the different polarizations of the two images).
201:, because of its historical ambiguity, should be avoided in original writing. One can easily specify the orientation of a particular field vector; and even the term
470:, the wave-normal direction, and the ray direction are all in the same plane, and it is all the more natural to define that plane as the "plane of polarization".
1310:, vol. 1 (1866), pp. 609–48; translated as "On the calculation of the tints that polarization develops in crystalline plates, & postscript",
897:
illustrate, one would pay attention to the electric vectors and assume that the "plane" of polarization (if one needed such a concept) contained those vectors.
808:(lower stiffness). To obtain results that agreed with observations on partial reflection, they had to suppose, contrary to Fresnel, that the vibrations were
580:
of a calcite crystal as a plane normal to a natural surface and parallel to the axis of the obtuse solid angle. This axis was parallel to the axes of the
1743:
1043:
Concerning the limitations of elastic-electromagnetic analogies, see (e.g.) Born & Wolf, 1970, pp. xxiv–xxv; Darrigol, 2012, pp. 227–32.
761:
and a direction of propagation. In Fig. 1, the only plane meeting that specification is the one labeled "Plane of vibration" and later numbered
143:
in 1811, the plane of polarization coincided (although this was not known at the time) with the plane containing the direction of propagation and the
170:
direction, because these directions generally differ and are both perpendicular to the magnetic vector (Fig. 1). Malus, as an adherent of the
403:'s lecture on polarization. In the latter case one must infer the convention from the context: Feynman keeps emphasizing the direction of the
533:(2) the plane containing both magnetic vectors and both propagation directions (i.e., the plane normal to the electric vectors).
499:(1) the plane containing both electric vectors and both propagation directions (i.e., the plane normal to the magnetic vectors);
162:(doubly-refractive) crystal, under the old definition, one must also specify whether the direction of propagation means the ray direction (
815:
1718:, University of Chicago Press, 1912; Project Gutenberg, 2005. (Cited page numbers match the 1912 edition and the Gutenberg HTML edition.)
617:
of a polarized ray as the plane, containing the ray, in which a principal section of a calcite crystal must lie in order to cause only
804:
avoided this complication by supposing that a higher refractive index corresponded always to the same density but a greater elastic
194:, is perpendicular to Fresnel's "plane of polarization" but identical with the plane that modern writers tend to call by that name!
17:
947:
There is also a context in which the original definition might still suggest itself. In a non-magnetic non-chiral crystal of the
1114:
833:
as "the plane passing through the ray and the direction of vibration" (in agreement with Fig. 1). Now suppose that a fine
738:
The vibrations normal to Malus's plane of polarization are electric, and the electric vibration tangential to the wavefront is
1702:
1548:
1026:
The actual writing of this treatise (Fresnel, 1822) was apparently completed by mid 1821; see I. Grattan-Guinness,
1815:
825:
The question called for an experimental determination of the direction of vibration, and the challenge was answered by
364:
properties of media than to differences in their magnetic properties. That circumstance tends to draw attention to the
1302:
A. Fresnel, "Note sur le calcul des teintes que la polarisation développe dans les lames cristallisées" et seq.,
1745:
A History of the
Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century
1533:
1477:
186:
medium such as air, the ray and wave-normal directions are the same, and
Fresnel's modification makes no difference.
529:
have the same direction, so that the ray and wave-normal directions merge, and the planes (2a) and (2b) become one:
1774:
694:
is in fact light whose orientation is rapidly and randomly changing. Supposing that light waves were analogous to
852:
838:
MacCullagh and
Neumann said), they will be crowded in the same direction; and if the planes of polarization are
826:
1810:
584:
1722:
884:
vibrations because of their interactions with matter, whereas the old "plane of polarization" contained the
504:(2a) the plane containing the magnetic vectors and the wave-normal (i.e., the plane normal to
1825:
171:
742:(Fig. 1). Thus, in terms of the above numbering, Fresnel changed the "plane of polarization" from
1830:
1753:
1667:(London: Taylor & Francis, 1852), pp. 238–333. (Cited page numbers are from the translation.)
1281:
1723:"On the demonstration of Fresnel's formulas for reflected and refracted light; and their applications"
1391:
1820:
1767:
778:
The principle that refractive index depended on the density of the aether was essential to
Fresnel's
276:
97:
151:, if it is used at all, is likely to mean the plane containing the direction of propagation and the
1805:
1526:
The Rise of the Wave Theory of Light: Optical Theory and
Experiment in the Early Nineteenth Century
1433:, vol. 21 (1995), pp. 149–62. (Note that the authors' analogy is only two-dimensional.)
513:(2b) the plane containing the magnetic vectors and the ray (i.e., the plane normal to
949:
77:. Malus's original "plane of polarization" was the plane containing the magnetic vectors and the
779:
117:
1656:
1652:
1633:
1625:
1621:
1613:
1605:
1601:
1593:
1589:
1160:
640:
vectors is still found in the definition given in the online Merriam-Webster dictionary. Even
605:
458:, hence the same angle between the ray direction and the wave-normal direction (Fig. 1).
412:
140:
675:
641:
175:
132:
1577:
688:
polarized in the sense of having a particular transverse orientation, and that what we call
450:
and the magnetic vectors; but there is generally a small angle between the electric vectors
1648:
1565:
Supplément à la traduction française de la cinquième édition du "Système de Chimie" par Th.
1517:
699:
349:
341:
179:
30:
859:(both being directional). The result is that the velocity of the solid corresponds to the
8:
1507:
1009:
970:
834:
801:
711:
474:
323:
240:
direction (the ray direction and wave-normal direction), with the electric field vectors
122:
975:
863:
field, so that the mechanical vibrations of the shear wave are in the direction of the
843:
manner. Stokes performed such an experiment in 1849, and it found in favor of Fresnel.
622:
558:
481:
was coined about 50 years earlier, and the associated mystery dates back even further.
387:
antenna. In this case the stated polarization refers to the alignment of the electric (
155:
vector, because the electric field has the greater propensity to interact with matter.
1580:; translated by T. Young as "Elementary view of the undulatory theory of light",
1512:, 2nd Ed., Cambridge: Deighton, Bell, & Co. / London: George Bell & Sons.
1698:
1544:
1529:
1473:
690:
167:
995:
935:
797:
703:
473:
This "natural" definition, however, depends on the theory of EM waves developed by
287:
105:
587:
by which he (correctly) explained the directions of the extraordinary refraction.
446:
and the magnetic vectors, and the wave-normal direction is still perpendicular to
333:-polarized wave), the orientations of the field vectors are fixed (Fig. 2).
1800:
1739:
1687:
1683:
1679:
1563:
1426:
855:(both being non-directional), and the compliance must correspond to the electric
680:
442:
are still perpendicular to both, and the ray direction is still perpendicular to
400:
163:
113:
109:
1193:
1013:, after its dependence on the refractive index was determined experimentally by
542:
1795:
1779:
1014:
954:
721:
Fresnel himself found this implication inconvenient; later that year he wrote:
391:) field, hence the alignment of the closely spaced metal ribs in the reflector.
345:
299:
284:
127:
953:
class (in which there is no ordinary refraction, but both refractions violate
283:
medium (that is, a medium whose properties are independent of direction), the
139:
Unfortunately the two conventions are contradictory. As originally defined by
1789:
1451:
Indeed this is the only context in which Hecht (5th Ed., 2017) uses the term
867:
vibrations of the EM wave. But Stokes's experiments were bound to detect the
561:, as he investigated the double refraction of "Iceland crystal" (transparent
423:
159:
910:
856:
644:, having said that "It is customary to define the polarization in terms of
566:
1007:
The angle of reflection at which this modification occurs became known as
1071:
656:
and the axis of propagation." That definition is identical with Malus's.
1714:
353:
337:
909:
suggest, by specifying the "plane of vibration" of that vector.
590:
372:
1398:, vol. 9, part 1 (1851), pp. 1–62, at pp. 4–5.
1066:
J.G. Lunney and D. Weaire, "The ins and outs of conical refraction",
906:
783:
757:
What Fresnel called the "more natural" choice was a plane containing
384:
319:
229:
1651:; reprinted as "Second mémoire…" in Fresnel, 1866–70, vol. 2,
1316:
1541:
A History of Optics: From Greek Antiquity to the Nineteenth Century
1070:, vol. 37, no. 3 (May–June 2006), pp. 26–9,
902:
664:
636:
above. The implication that the plane of polarization contains the
581:
183:
1641:
Mémoires de l'Académie Royale des Sciences de l'Institut de France
1095:
Stratton, 1941, p. 280; Born & Wolf, 1970, pp. 43,
847:
vibrations of that light can only be perpendicular to that plane.
632:
The plane of the ray and the magnetic vectors is the one numbered
178:, in his successful effort to explain double refraction under the
1246:
Buchwald, 1989, pp. 31–43; Darrigol, 2012, pp. 191–2.
707:
562:
1674:
H. de Senarmont, E. Verdet, and L. Fresnel), 1866–70,
1407:
Powell, 1856, pp. 19–20; Whittaker, 1910, pp. 168–9.
1311:
695:
557:
Polarization was discovered — but not named or understood — by
1729:, Series 4, vol. 12, no. 76, pp. 1–20.
1188:, California Institute of Technology, 1963–2013, Volume
357:
93:
1378:
Powell, 1856, pp. 4–5; Whittaker, 1910, p. 149.
925:
and the wave-normal, in agreement with Fig. 1 above.
880:
The electromagnetic theory of light further emphasized the
1712:(Leiden: Van der Aa), translated by S.P. Thompson as
678:
announced his hypothesis that light waves are exclusively
217:
418:
If the medium is magnetically isotropic but electrically
629:
vectors of the polarized ray, not the electric vectors.
1419:
108:
spanned by the direction of propagation and either the
1639:
A. Fresnel, 1827, "Mémoire sur la double réfraction",
1572:, Paris: Chez Méquignon-Marvis, 1822, pp. 1–137,
1751:
116:, depending on the convention. It can be defined for
1576:
535–9; reprinted in Fresnel, 1866–70, vol. 2,
1062:
1060:
1396:
Transactions of the Cambridge Philosophical Society
790:a birefringent medium, plus a variation in density
271:
medium is more complicated; cf. Fig. 1.)
1509:A Chapter on Fresnel's Theory of Double Refraction
1472:, 4th Ed., New York: McGraw-Hill, 1976,
1462:
569:). The essence of his discovery, published in his
395:Indeed, that is the convention used in the online
1582:Quarterly Journal of Science, Literature, and Art
1237:Huygens, 1690, tr. Thompson, pp. 55–6.
1228:Huygens, 1690, tr. Thompson, pp. 92–4.
1057:
994:This conclusion does not follow if the medium is
773:
770:vibrations was the subject of continuing debate.
1787:
1184:R.P. Feynman, R.B. Leighton, and M. Sands,
88: and Malus's plane merges with Fresnel's.)
1678:(3 volumes), Paris: Imprimerie Impériale;
1386:
1384:
1180:
1178:
1172:Born & Wolf, 1970, pp. 28, 43.
318:direction (the direction perpendicular to the
1727:Philosophical Magazine and Journal of Science
1296:
1147:Fresnel, 1827, tr. Hobson, p. 318.
1028:Convolutions in French Mathematics, 1800–1840
434:are still parallel, and the electric vectors
1159:Fresnel, 1822, tr. Young, part 7,
1381:
1276:
1274:
1175:
174:, could only choose the ray direction. But
1480:, pp. 553–4, including Fig. 26
360:) is more often due to differences in the
252:direction, and the magnetic field vectors
1427:"On the acoustic-electromagnetic analogy"
1315:
1392:"On the dynamical theory of diffraction"
1271:
1082:
1080:
814:
663:
589:
541:
371:
216:
29:
1521:, 4th Ed., Oxford: Pergamon Press.
1468:Cf. F.A. Jenkins and H.E. White,
1206:
1204:
1202:
1155:
1153:
1143:
1141:
1109:
1107:
1105:
147:vector. In modern literature, the term
81:. (In an isotropic medium,
14:
1788:
1131:
1129:
1127:
484:
212:
1077:
264:direction. (The situation in a
228:Linearly-polarized (plane-polarized)
1748:, London: Longmans, Green, & Co.
1676:Oeuvres complètes d'Augustin Fresnel
1655:; translated by A.W. Hobson as
1308:Oeuvres complètes d'Augustin Fresnel
1264:Born & Wolf, 1970, pp. 43,
1219:Born & Wolf, 1970, p. 668.
1199:
1150:
1138:
1102:
921:), which he defines as the plane of
383:Vertically polarized parabolic-grid
205:carries less risk of confusion than
1562:), in J. Riffault (ed.),
1493:Born & Wolf, 1970, p. 43.
1347:Aldis, 1879, pp. 9, 20.
1135:Born & Wolf, 1970, p. 28.
1124:
659:
489:
24:
1416:Whittaker, 1910, pp. 169–70.
1284:, accessed 15 September 2017.
1121:, accessed 15 September 2017.
875:
820:George Gabriel Stokes (1819–1903).
669:Augustin-Jean Fresnel (1788–1827).
336:Because innumerable materials are
120:light, remains fixed in space for
25:
1842:
1628:; vol. 26 (Jan.– Jun.
1616:; vol. 25 (Jul.– Dec.
1608:; vol. 24 (Jan.– Jun.
1596:; vol. 23 (Jul.– Dec.
1584:, vol. 22 (Jan.– Jun.
1356:Darrigol, 2012, pp. 258–60.
928:
537:
197:It has been argued that the term
1773:
1761:
1425:J.M. Carcione and F. Cavallini,
1304:Annales de Chimie et de Physique
1293:Buchwald, 1989, pp. 227–9.
595:Étienne-Louis Malus (1775–1812).
477:in the 1860s — whereas the word
298:) are in one direction, and the
1528:, University of Chicago Press,
1500:
1487:
1445:
1436:
1410:
1401:
1372:
1365:Whittaker, 1910, pp. 127,
1359:
1350:
1341:
1332:
1323:
1287:
1258:
1249:
1240:
1231:
1222:
1213:
1186:The Feynman Lectures on Physics
1037:
1030:, Basel: Birkhäuser, 1990, vol.
1020:
1001:
988:
426:crystal), the magnetic vectors
1697:, 5th Ed., Pearson Education,
1394:(read 26 November 1849),
1166:
1089:
13:
1:
1657:"Memoir on double refraction"
1329:Darrigol, 2012, p. 212.
1210:Stratton, 1941, p. 280.
1050:
944:causes no further confusion.
1721:B. Powell (July 1856),
1659:, in R. Taylor (ed.),
1255:Buchwald, 1989, p. 45.
1086:Buchwald, 1989, p. 54.
747:
743:
633:
344:while comparatively few are
7:
1515:M. Born and E. Wolf, 1970,
1338:Aldis, 1879, pp. 8–9.
1072:doi.org/10.1051/epn:2006305
964:
893:, then, as Feynman and the
812:the plane of polarization.
762:
751:
236:medium, propagating in the
232:electromagnetic wave in an
172:corpuscular theory of light
10:
1847:
1647:(for 1824, printed 1827),
1442:Hecht, 2017, p. 338.
277:electromagnetic (EM) waves
1816:Electromagnetic radiation
1320:(Creative Commons), 2021.
706:corresponded to a higher
98:electromagnetic radiation
1736:, New York: McGraw-Hill.
1688:vol. 3 (1870)
1684:vol. 2 (1868)
1680:vol. 1 (1866)
981:
765:— that is, the one that
521:In an isotropic medium,
18:Direction of propagation
1282:"Plane of polarization"
1280:Merriam-Webster, Inc.,
1119:Encyclopædia Britannica
397:Encyclopædia Britannica
356:of EM waves (including
1734:Electromagnetic Theory
1470:Fundamentals of Optics
913:also prefers the term
822:
780:aether drag hypothesis
671:
597:
554:
392:
272:
89:
1732:J.A. Stratton, 1941,
1524:J.Z. Buchwald, 1989,
1453:plane of polarization
1113:M. Luntz (?) et al.,
942:plane of polarization
827:George Gabriel Stokes
818:
676:Augustin-Jean Fresnel
667:
642:Julius Adams Stratton
615:plane of polarization
593:
545:
375:
220:
207:plane of polarization
199:plane of polarization
176:Augustin-Jean Fresnel
149:plane of polarization
126:light, and undergoes
102:plane of polarization
33:
1811:Polarization (waves)
1710:Traité de la Lumière
1518:Principles of Optics
1074:, at pp. 26–7.
774:"Plane of vibration"
702:, and that a higher
329:wave (also called a
133:circularly-polarized
1539:O. Darrigol, 2012,
1115:"Double refraction"
971:E-plane and H-plane
917:(or, more usually,
835:diffraction grating
802:Franz Ernst Neumann
712:luminiferous aether
606:Étienne-Louis Malus
485:History of the term
475:James Clerk Maxwell
422:-isotropic (like a
213:Physics of the term
141:Étienne-Louis Malus
1826:History of physics
1768:History of science
1708:C. Huygens, 1690,
1661:Scientific Memoirs
1554:A. Fresnel, 1822,
1506:W.S. Aldis, 1879,
996:optically rotating
976:Plane of incidence
919:plane-of-vibration
915:plane of vibration
831:plane of vibration
823:
672:
623:plane of incidence
598:
576:Huygens defined a
559:Christiaan Huygens
555:
393:
314:direction and the
273:
203:plane of vibration
192:plane of vibration
123:linearly-polarized
90:
1831:Planes (geometry)
1715:Treatise on Light
1703:978-1-292-09693-3
1653:pp. 479–596
1632:1829), pp.
1620:1828), pp.
1612:1828), pp.
1600:1827), pp.
1588:1827), pp.
1549:978-0-19-964437-7
829:. He defined the
691:unpolarized light
578:principal section
571:Treatise on Light
424:doubly-refracting
69: &
61: &
27:Concept in optics
16:(Redirected from
1838:
1821:Antennas (radio)
1778:
1777:
1766:
1765:
1764:
1757:
1693:E. Hecht, 2017,
1673:
1666:
1649:pp. 45–176
1646:
1631:
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1182:
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1148:
1145:
1136:
1133:
1122:
1111:
1100:
1098:
1093:
1087:
1084:
1075:
1068:Europhysics News
1064:
1044:
1041:
1035:
1034:2, p. 884.
1033:
1024:
1018:
1010:Brewster's angle
1005:
999:
992:
933:In an optically
798:James MacCullagh
704:refractive index
660:Fresnel's choice
652:containing both
552:
490:Three candidates
461:
415:(Fig. 3).
382:
270:
227:
87:
40:
21:
1846:
1845:
1841:
1840:
1839:
1837:
1836:
1835:
1806:Physical optics
1786:
1785:
1784:
1772:
1762:
1760:
1752:
1740:E. T. Whittaker
1671:
1670:A. Fresnel (ed.
1664:
1644:
1629:
1617:
1609:
1597:
1585:
1578:pp. 3–146
1573:
1566:
1503:
1498:
1497:
1492:
1488:
1481:
1467:
1463:
1456:
1455:(pp. 386,
1450:
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1437:
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1250:
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1241:
1236:
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1227:
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1214:
1209:
1200:
1194:Lecture 33
1189:
1183:
1176:
1171:
1167:
1158:
1151:
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1125:
1112:
1103:
1096:
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1090:
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1058:
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1047:
1042:
1038:
1031:
1025:
1021:
1006:
1002:
993:
989:
984:
967:
931:
878:
876:Modern practice
821:
776:
718:to that plane!
670:
662:
596:
585:secondary waves
550:
540:
492:
487:
459:
380:
265:
225:
215:
164:Poynting vector
158:For waves in a
114:magnetic vector
110:electric vector
82:
41:Field vectors (
38:
28:
23:
22:
15:
12:
11:
5:
1844:
1834:
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1174:
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1149:
1137:
1123:
1101:
1088:
1076:
1055:
1054:
1052:
1049:
1046:
1045:
1036:
1019:
1015:David Brewster
1000:
986:
985:
983:
980:
979:
978:
973:
966:
963:
930:
929:Remaining uses
927:
877:
874:
819:
786:of the aether
775:
772:
732:
731:
730:
729:
700:elastic solids
684:and therefore
668:
661:
658:
604:was coined by
594:
539:
538:Malus's choice
536:
535:
534:
519:
518:
510:
509:
501:
500:
491:
488:
486:
483:
300:magnetic field
285:electric field
214:
211:
166:) or the wave-
128:axial rotation
26:
9:
6:
4:
3:
2:
1843:
1832:
1829:
1827:
1824:
1822:
1819:
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1711:
1707:
1704:
1700:
1696:
1692:
1689:
1685:
1681:
1677:
1669:
1663:, vol.
1662:
1658:
1654:
1650:
1643:, vol.
1642:
1638:
1635:
1627:
1623:
1615:
1607:
1603:
1595:
1591:
1583:
1579:
1571:
1570:
1561:
1557:
1556:De la Lumière
1553:
1550:
1546:
1542:
1538:
1535:
1534:0-226-07886-8
1531:
1527:
1523:
1520:
1519:
1514:
1511:
1510:
1505:
1504:
1490:
1479:
1478:0-07-032330-5
1475:
1471:
1465:
1454:
1448:
1439:
1432:
1428:
1422:
1413:
1404:
1397:
1393:
1390:G.G. Stokes,
1387:
1385:
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764:
760:
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753:
749:
745:
741:
736:
728:appellations.
726:
725:
724:
723:
722:
719:
717:
716:perpendicular
713:
709:
705:
701:
697:
693:
692:
687:
683:
682:
677:
666:
657:
655:
651:
647:
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624:
620:
616:
612:
607:
603:
592:
588:
586:
583:
579:
574:
572:
568:
565:, now called
564:
560:
548:
544:
532:
531:
530:
528:
524:
516:
512:
511:
507:
503:
502:
498:
497:
496:
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480:
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453:
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437:
433:
429:
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410:
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402:
398:
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386:
378:
374:
370:
367:
363:
359:
355:
351:
347:
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339:
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326:
321:
317:
313:
309:
305:
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297:
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111:
107:
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99:
95:
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76:
72:
68:
64:
60:
56:
52:
48:
44:
36:
32:
19:
1744:
1733:
1726:
1713:
1709:
1694:
1675:
1660:
1640:
1581:
1564:
1559:
1555:
1540:
1525:
1516:
1508:
1501:Bibliography
1489:
1469:
1464:
1452:
1447:
1438:
1430:
1421:
1412:
1403:
1395:
1374:
1361:
1352:
1343:
1334:
1325:
1307:
1303:
1298:
1289:
1260:
1251:
1242:
1233:
1224:
1215:
1185:
1168:
1161:p. 406
1118:
1091:
1067:
1039:
1027:
1022:
1008:
1003:
990:
959:
948:
946:
941:
934:
932:
922:
918:
914:
899:
894:
890:
885:
881:
879:
868:
864:
860:
857:permittivity
853:permeability
849:
845:
839:
830:
824:
809:
805:
796:
791:
787:
777:
766:
758:
756:
739:
737:
733:
720:
715:
689:
685:
679:
673:
653:
649:
645:
637:
631:
626:
618:
614:
610:
602:polarization
601:
599:
577:
575:
570:
567:Iceland spar
556:
547:Fig. 4
546:
526:
522:
520:
514:
505:
493:
479:polarization
478:
472:
467:
463:
455:
451:
447:
443:
439:
435:
431:
427:
419:
417:
408:
404:
396:
394:
388:
377:Fig. 3
376:
365:
361:
346:ferromagnets
335:
330:
324:
315:
311:
307:
303:
295:
291:
280:
274:
266:
261:
257:
253:
249:
245:
241:
237:
233:
222:Fig. 2
221:
206:
202:
198:
196:
191:
188:
160:birefringent
157:
152:
148:
144:
138:
131:
121:
101:
91:
83:
78:
74:
70:
66:
62:
58:
54:
50:
46:
42:
35:Fig. 1
34:
1431:Wave Motion
955:Snell's law
696:shear waves
338:dielectrics
316:wave-normal
180:wave theory
75:wave-normal
1790:Categories
1543:, Oxford,
1051:References
895:Britannica
806:compliance
681:transverse
582:spheroidal
354:refraction
350:reflection
342:conductors
327:-polarized
269:-isotropic
230:sinusoidal
96:and other
73:) and the
784:stiffness
674:In 1821,
600:The term
399:, and in
385:microwave
322:). For a
320:wavefront
302:vectors (
281:isotropic
234:isotropic
184:isotropic
118:polarized
1742:, 1910,
1560:On Light
1017:in 1815.
965:See also
886:magnetic
882:electric
869:electric
865:magnetic
638:magnetic
627:magnetic
619:ordinary
413:antennas
405:electric
366:electric
362:electric
325:linearly
153:electric
145:magnetic
53:,
49:,
45:,
1780:Physics
1754:Portals
1672:
1630:
1626:389–407
1618:
1614:198–215
1610:
1598:
1586:
1574:
1569:Thomson
1567:
1457:
1367:
1317:4058004
1314::
1266:
1097:
1032:
950:biaxial
794:media.
792:between
710:of the
708:density
563:calcite
460:
401:Feynman
288:vectors
260:in the
248:in the
136:light.
112:or the
104:is the
1801:Optics
1701:
1695:Optics
1634:159–65
1622:168–91
1606:431–48
1602:113–35
1594:441–54
1590:127–41
1547:
1532:
1476:
1369:132–5.
1312:Zenodo
936:chiral
840:normal
810:within
788:within
767:modern
686:always
551:
462:Hence
381:
348:, the
279:in an
226:
168:normal
100:, the
39:
1796:Light
1459:392).
982:Notes
911:Hecht
891:alone
358:light
331:plane
106:plane
94:light
1699:ISBN
1545:ISBN
1530:ISBN
1474:ISBN
1268:681.
1099:681.
907:Wolf
905:and
903:Born
800:and
748:(2a)
744:(2b)
634:(2b)
525:and
454:and
438:and
430:and
306:and
294:and
275:For
256:and
244:and
130:for
92:For
1645:VII
763:(1)
752:(2)
746:to
698:in
611:one
420:non
352:or
340:or
312:ray
267:non
86:= 0
79:ray
1792::
1725:,
1686:,
1682:,
1624:,
1604:,
1592:,
1429:,
1383:^
1273:^
1201:^
1192:,
1177:^
1152:^
1140:^
1126:^
1117:,
1104:^
1079:^
1059:^
754:.
517:).
508:);
466:,
209:.
1756::
1705:.
1690:.
1665:V
1636:.
1558:(
1551:.
1536:.
1484:.
1482:I
1196:.
1190:I
1163:.
923:E
861:H
759:D
740:D
654:H
650:E
646:E
549::
527:D
523:E
515:E
506:D
468:E
464:D
456:D
452:E
448:D
444:E
440:D
436:E
432:H
428:B
409:E
407:(
389:E
379::
308:H
304:B
296:D
292:E
290:(
262:z
258:H
254:B
250:y
246:D
242:E
238:x
224::
84:θ
71:H
67:B
63:D
59:E
55:H
51:B
47:D
43:E
37::
20:)
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