53:
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1921:"If a lens is thin, or if we can guess at the position of the principal planes, we can readily construct from the following simple rules that it is well to bear in mind. They refer specifically to the case of a positive lens forming a real image of a real object, all distances and the magnification being assumed to be positive quantities. If virtual images are involved, it is better to return to the original formulas, . The equations are ."
41:
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1829:(or micron bar) is a bar of stated length superimposed on a picture. When the picture is resized the bar will be resized in proportion. If a picture has a scale bar, the actual magnification can easily be calculated. Where the scale (magnification) of an image is important or relevant, including a scale bar is preferable to stating magnification.
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1824:
Magnification figures on pictures displayed in print or online can be misleading. Editors of journals and magazines routinely resize images to fit the page, making any magnification number provided in the figure legend incorrect. Images displayed on a computer screen change size based on the size of
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which consists of a
Ramsden eyepiece with micrometer hairs in the back focal plane. This is mounted in front of the telescope eyepiece and used to evaluate the diameter of the exit pupil. This will be much smaller than the object glass diameter, which gives the linear magnification (actually a
1775:
With any telescope or microscope, or a lens a maximum magnification exists beyond which the image looks bigger but shows no more detail. It occurs when the finest detail the instrument can resolve is magnified to match the finest detail the eye can see. Magnification beyond this maximum is
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1107:
in centimeters. The constant 25 cm is an estimate of the "near point" distance of the eye—the closest distance at which the healthy naked eye can focus. In this case the angular magnification is independent from the distance kept between the eye and the magnifying glass.
415:, where the size of the object is a linear dimension and the apparent size is an angle, the magnification is the ratio between the apparent (angular) size as seen in the eyepiece and the angular size of the object when placed at the conventional closest distance of distinct vision:
1019:
depends on how the glass and the object are held, relative to the eye. If the lens is held at a distance from the object such that its front focal point is on the object being viewed, the relaxed eye (focused to infinity) can view the image with angular magnification
342:
169:, which makes a small object appear as a much larger image at a comfortable distance for viewing. A microscope is similar in layout to a telescope except that the object being viewed is close to the objective, which is usually much smaller than the eyepiece.
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Measuring the actual angular magnification of a telescope is difficult, but it is possible to use the reciprocal relationship between the linear magnification and the angular magnification, since the linear magnification is constant for all objects.
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55:
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A different interpretation of the working of the latter case is that the magnifying glass changes the diopter of the eye (making it myopic) so that the object can be placed closer to the eye resulting in a larger angular magnification.
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If instead the lens is held very close to the eye and the object is placed closer to the lens than its focal point so that the observer focuses on the near point, a larger angular magnification can be obtained, approaching
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The telescope is focused correctly for viewing objects at the distance for which the angular magnification is to be determined and then the object glass is used as an object the image of which is known as the
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where black dimensions are real, grey are virtual. The direction of the arrows can be used to describe cartesian +/− signage: from the centre of the lens, left or down = negative, right or up = positive.
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1001:{\displaystyle {\begin{aligned}M&={d_{\mathrm {i} } \over d_{\mathrm {o} }}={h_{\mathrm {i} } \over h_{\mathrm {o} }}\\&={f \over d_{\mathrm {o} }-f}={d_{\mathrm {i} }-f \over f}\end{aligned}}}
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Note that both astronomical telescopes as well as simple microscopes produce an inverted image, thus the equation for the magnification of a telescope or microscope is often given with a
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Stepwise magnification by 6% per frame into a 39-megapixel image. In the final frame, at about 170x, an image of a bystander is seen reflected in the man's
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of that angle (in practice, this makes a difference only if the angle is larger than a few degrees). Thus, angular magnification is given by:
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corresponding to a magnification of around 1200×. Without oil immersion, the maximum usable magnification is around 800×. For details, see
1809:
Small, cheap telescopes and microscopes are sometimes supplied with the eyepieces that give magnification far higher than is usable.
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203:. Optical magnification is sometimes referred to as "power" (for example "10× power"), although this can lead to confusion with
337:{\displaystyle M_{A}={\frac {\tan \varepsilon }{\tan \varepsilon _{0}}}\approx {\frac {\varepsilon }{\varepsilon _{0}}}}
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For a good quality telescope operating in good atmospheric conditions, the maximum usable magnification is limited by
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1889:
1881:
Applied
Photographic Optics: Lenses and Optical Systems for Photography, Film, Video, Electronic and Digital Imaging
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is the ratio between the apparent size of an object (or its size in an image) and its true size, and thus it is a
20:
158:
to create an image of a distant object and then allows the user to examine the image closely with a smaller
1783:. In practice it is considered to be 2× the aperture in millimetres or 50× the aperture in inches; so, a
1761:{\displaystyle M_{\mathrm {A} }={1 \over M}={D_{\mathrm {Objective} } \over {D_{\mathrm {Ramsden} }}}\,.}
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and positive. Only if the focal length is negative, the image's height, distance and magnification are
773:{\displaystyle M=-{d_{\mathrm {i} } \over d_{\mathrm {o} }}={h_{\mathrm {i} } \over h_{\mathrm {o} }}}
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and positive. When the focal length is positive the image's height, distance and magnification are
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8:
78:, not physical size, of something. This enlargement is quantified by a size ratio called
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will also be negative. However, the traditional sign convention used in photography is "
82:. When this number is less than one, it refers to a reduction in size, sometimes called
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the magnification of the eyepiece. The magnification of the objective depends on its
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The maximum relative to the minimum magnification of an optical system is known as
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is the angle subtended by the object at the front focal point of the objective and
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and is usually inverted. When measuring the height of an inverted image using the
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to make things look bigger by allowing the user to hold them closer to their eye.
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is negative". Therefore, in photography: Object height and distance are always
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1640:. The diameter of this may be measured using an instrument known as a Ramsden
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and is calculated by the same equation as that of a magnifying glass (above).
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is the angle subtended by the image at the rear focal point of the eyepiece.
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with 10× magnification, the Moon appears to subtend an angle of about 5.2°.
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1529:{\displaystyle M_{\mathrm {A} }={f_{\mathrm {o} } \over f_{\mathrm {e} }}}
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1244:{\displaystyle M_{\mathrm {A} }=M_{\mathrm {o} }\times M_{\mathrm {e} }}
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1909:. Bellingham, Washington: SPIE Optical Engineering Press. p. 32.
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sign convention (where the x-axis is the optical axis) the value for
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400:'s disk as viewed from Earth's surface is about 0.52°. Thus, through
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Note again that a negative magnification implies an inverted image.
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the height of the object, the magnification can also be written as:
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The maximum angular magnification (compared to the naked eye) of a
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means a linear dimension (measured, for example, in millimeters or
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115:. In all cases, the magnification of the image does not change the
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The magnification of the eyepiece depends upon its focal length
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diameter telescope has a maximum usable magnification of 120×.
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64:
1168:{\displaystyle M_{\mathrm {A} }={25\ \mathrm {cm} \over f}+1}
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reduction), the angular magnification can be determined from
96:
1070:{\displaystyle M_{\mathrm {A} }={25\ \mathrm {cm} \over f}}
251:
means the angle subtended by the object at the focal point (
131:
provide visual aid by magnifying small or distant subjects.
1417:{\displaystyle M_{\mathrm {o} }={d \over f_{\mathrm {o} }}}
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243:, the linear dimension of the image seen in the eyepiece (
26:"Magnify" redirects here. For the Ham Sandwich album, see
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493:{\displaystyle M={f \over f-d_{\mathrm {o} }}}
247:at infinite distance) cannot be given, thus
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396:For example, the mean angular size of the
255:). Strictly speaking, one should take the
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1776:sometimes called "empty magnification".
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1627:Measurement of telescope magnification
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1820:"Magnification" of displayed images
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33:. For the film sales company, see
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21:Magnification (disambiguation)
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1612:{\textstyle f_{\mathrm {e} }}
1560:{\textstyle f_{\mathrm {o} }}
1448:{\textstyle f_{\mathrm {e} }}
1336:{\textstyle f_{\mathrm {o} }}
1304:{\textstyle M_{\mathrm {e} }}
1275:{\textstyle M_{\mathrm {o} }}
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839:and negative. Therefore, the
686:{\textstyle h_{\mathrm {o} }}
657:{\textstyle h_{\mathrm {i} }}
628:{\textstyle d_{\mathrm {i} }}
548:{\textstyle d_{\mathrm {o} }}
366:{\textstyle \varepsilon _{0}}
1771:Maximum usable magnification
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664:the height of the image and
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1905:Kingslake, Rudolph (1992).
1884:. Focal Press. p. 40.
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1619:is the focal length of the
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1371:(called the tube length):
842:photographic magnification
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386:{\textstyle \varepsilon }
123:Examples of magnification
790:The image recorded by a
1878:Ray, Sidney F. (2002).
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834:
830:
811:
787:
784:
764:
759:
752:
747:
741:
733:
728:
721:
716:
710:
707:
704:
679:
674:
650:
645:
621:
616:
596:{\textstyle M}
592:
581:virtual images
572:{\textstyle M}
568:
541:
536:
515:{\textstyle f}
511:
483:
478:
474:
471:
467:
462:
459:
441:
438:
436:
433:
419:from the eye.
382:
360:
356:
329:
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321:
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308:
304:
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297:
292:
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286:
280:
275:
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232:
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212:
209:
193:
190:
189:
188:
181:
170:
163:
156:primary mirror
152:objective lens
144:
124:
121:
119:of the image.
15:
9:
6:
4:
3:
2:
1950:
1939:
1936:
1935:
1933:
1918:
1916:0-8194-0763-1
1912:
1908:
1901:
1893:
1891:0-240-51540-4
1887:
1883:
1882:
1874:
1870:
1860:
1857:
1855:
1852:
1850:
1847:
1845:
1842:
1840:
1837:
1836:
1830:
1828:
1817:
1815:
1810:
1807:
1805:
1797:
1796:oil immersion
1793:
1788:
1782:
1777:
1768:
1755:
1722:
1685:
1679:
1674:
1671:
1666:
1655:
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1639:
1633:
1624:
1622:
1598:
1589:
1585:
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1513:
1501:
1495:
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1463:
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1456:
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1401:
1397:
1392:
1381:
1372:
1370:
1366:
1350:
1322:
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1261:
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1230:
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1191:
1189:
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1109:
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989:
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944:
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914:
902:
896:
883:
871:
865:
863:
858:
846:
844:
836:
832:
828:
826:
823:is positive,
822:
810:
805:
801:
797:
793:
783:
780:
757:
745:
739:
726:
714:
708:
705:
702:
694:
672:
643:
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604:
590:
582:
566:
558:
534:
525:
509:
500:
476:
472:
469:
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460:
457:
449:
447:
435:By instrument
429:
424:
420:
414:
410:
405:
403:
399:
394:
380:
358:
354:
344:
327:
323:
319:
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258:
254:
250:
246:
245:virtual image
242:
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208:
206:
205:optical power
202:
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186:
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118:
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110:
106:
102:
98:
94:
89:
87:
86:
81:
77:
76:apparent size
73:
72:Magnification
66:
47:
42:
36:
32:
30:
22:
1906:
1900:
1880:
1873:
1826:
1823:
1813:
1811:
1808:
1789:
1778:
1774:
1647:
1634:
1630:
1569:focal length
1537:
1476:
1474:is given by
1469:
1457:
1425:
1373:
1313:focal length
1252:
1192:
1190:is given by
1185:
1176:
1114:
1110:
1101:focal length
1078:
1022:
1014:
847:
840:
808:
798:is always a
796:image sensor
789:
781:
695:
605:
524:focal length
501:
450:
443:
411:and optical
406:
395:
345:
261:
253:angular size
248:
234:
220:
214:
196:
195:
126:
90:
84:
83:
79:
71:
70:
28:
1800:200 nm
1781:diffraction
1365:focal plane
786:Photography
557:real images
440:Single lens
413:microscopes
217:real images
180:is similar.
117:perspective
1865:References
1849:Microscope
1814:zoom ratio
1794:and using
1785:60 mm
1638:exit pupil
1582:or of the
1460:minus sign
1188:microscope
1182:Microscope
800:real image
417:25 cm
402:binoculars
167:microscope
105:microscope
101:resolution
1827:scale bar
1642:dynameter
1588:reflector
1580:refractor
1573:objective
1538:in which
1466:Telescope
1227:×
983:−
956:−
804:cartesian
709:−
473:−
446:thin lens
428:Thin lens
381:ε
355:ε
324:ε
320:ε
315:≈
303:ε
299:
291:ε
288:
185:zoom lens
148:telescope
1932:Category
1833:See also
1621:eyepiece
1369:eyepiece
241:eyepiece
239:with an
178:enlarger
160:eyepiece
109:printing
103:, using
1571:of the
1567:is the
1367:of the
1103:of the
1099:is the
837:virtual
825:virtual
522:is the
257:tangent
93:visuals
31:(album)
29:Magnify
1938:Optics
1913:
1888:
1590:, and
1253:where
1143:
1079:Here,
1051:
502:where
346:where
225:inches
97:images
65:cornea
1586:in a
1578:in a
606:With
127:Some
1911:ISBN
1886:ISBN
1839:Lens
1576:lens
1105:lens
833:real
829:real
821:real
526:and
398:Moon
249:size
235:For
221:size
215:For
794:or
448:is
296:tan
285:tan
227:).
154:or
95:or
1934::
1816:.
1806:.
1623:.
1462:.
1140:25
1048:25
583:,
559:,
426:A
207:.
183:A
172:A
165:A
146:A
135:A
107:,
88:.
1919:.
1894:.
1756:.
1746:n
1743:e
1740:d
1737:s
1734:m
1731:a
1728:R
1723:D
1715:e
1712:v
1709:i
1706:t
1703:c
1700:e
1697:j
1694:b
1691:O
1686:D
1680:=
1675:M
1672:1
1667:=
1661:A
1656:M
1604:e
1599:f
1552:o
1547:f
1519:e
1514:f
1507:o
1502:f
1496:=
1490:A
1485:M
1440:e
1435:f
1407:o
1402:f
1398:d
1393:=
1387:o
1382:M
1351:d
1328:o
1323:f
1296:e
1291:M
1267:o
1262:M
1236:e
1231:M
1221:o
1216:M
1212:=
1206:A
1201:M
1163:1
1160:+
1155:f
1150:m
1147:c
1134:=
1128:A
1123:M
1087:f
1063:f
1058:m
1055:c
1042:=
1036:A
1031:M
990:f
986:f
977:i
972:d
965:=
959:f
950:o
945:d
940:f
935:=
920:o
915:h
908:i
903:h
897:=
889:o
884:d
877:i
872:d
866:=
859:M
817:M
812:i
809:h
763:o
758:h
751:i
746:h
740:=
732:o
727:d
720:i
715:d
706:=
703:M
678:o
673:h
649:i
644:h
620:i
615:d
591:M
567:M
540:o
535:d
510:f
482:o
477:d
470:f
466:f
461:=
458:M
359:0
328:0
307:0
279:=
274:A
270:M
67:.
48:.
37:.
23:.
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