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165:{\displaystyle a=2\arctan \left({\frac {D/2}{f}}\right)=2\arctan \left({\frac {D}{2f}}\right)}
347:
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close to 1, such as air, the angular aperture is approximately equal to twice the
330:{\displaystyle \mathrm {NA} =\sin a/2=\sin \arctan \left({\frac {D}{2f}}\right)}
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251:Formally, the numerical aperture in air is:
469:Acceptance angle, half the angular aperture
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405:{\displaystyle \mathrm {NA} \approx a/2}
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429:Albert Abraham Michelson (1995).
236:Relation to numerical aperture
1:
435:. Courier Dover. p. 32.
30:and an aperture of diameter
509:
20:The angular aperture of a
344:, with a small aperture,
406:
364:
363:{\displaystyle D<f}
342:paraxial approximation
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240:In a medium with an
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24:with focal point at
242:index of refraction
488:Geometrical optics
465:Numerical aperture
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246:numerical aperture
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188:
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52:
40:
432:Studies in Optics
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216:{\displaystyle D}
191:{\displaystyle f}
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70:as seen from the
43:{\displaystyle D}
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56:angular aperture
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473:Field of view
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442:0-486-68700-7
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248:of the lens.
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339:
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200:focal length
174:
66:of the lens
64:angular size
55:
53:
26:
25:
72:focal point
482:Categories
416:References
389:≈
302:
296:
276:
137:
97:
22:thin lens
460:f-number
454:See also
229:aperture
225:diameter
68:aperture
340:In the
227:of the
223:is the
198:is the
175:where
62:is the
439:
299:arctan
134:arctan
94:arctan
493:Angle
58:of a
437:ISBN
355:<
60:lens
54:The
293:sin
273:sin
484::
370::
74::
445:.
400:2
396:/
392:a
385:A
382:N
358:f
352:D
324:)
318:f
315:2
311:D
306:(
290:=
287:2
283:/
279:a
270:=
266:A
263:N
231:.
211:D
186:f
159:)
153:f
150:2
146:D
141:(
131:2
128:=
124:)
119:f
115:2
111:/
107:D
101:(
91:2
88:=
85:a
50:.
38:D
27:F
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