Angular aperture: Difference between revisions
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[[Image:Angular aperture.svg|right|The angular aperture of a [[thin lens]] with focal point at '''''F''''' and an aperture of diameter <math> |
[[Image:Angular aperture.svg|right|The angular aperture of a [[thin lens]] with focal point at '''''F''''' and an aperture of diameter <math>D</math>.|thumb|250px]] |
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The '''angular aperture''' of a [[lens (optics)|lens]] is the |
The '''angular aperture''' of a [[lens (optics)|lens]] is the [[angular size]] of the lens [[aperture]] as seen from the [[Focus (optics)|focal point]]: |
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:<math>a = 2 \arctan \left( \frac {D/2} {f} \right)</math> |
:<math>a = 2 \arctan \left( \frac {D/2} {f} \right) = 2 \arctan \left( \frac {D} {2f} \right)</math> |
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where |
where |
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== Relation to numerical aperture == |
== Relation to numerical aperture == |
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In a medium with an [[index of refraction]] close to 1, such as air, the angular aperture is approximately equal to twice the [[numerical aperture]] of the lens.<ref>{{cite book|title=Studies in Optics |author=Albert Abraham Michelson|year= 1995|publisher=Courier Dover|pages=32|isbn=0-486-68700-7|url= |
In a medium with an [[index of refraction]] close to 1, such as air, the angular aperture is approximately equal to twice the [[numerical aperture]] of the lens.<ref>{{cite book|title=Studies in Optics |author=Albert Abraham Michelson|year= 1995|publisher=Courier Dover|pages=32|isbn=0-486-68700-7|url= https://books.google.com/books?id=m2tUZ4_8WGMC&q=%22Angular+aperture%22&pg=PA32}}</ref> |
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Formally, the numerical aperture in air is: |
Formally, the numerical aperture in air is: |
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*[[f-number]] |
*[[f-number]] |
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*[[Numerical aperture]] |
*[[Numerical aperture]] |
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*Acceptance angle, half the angular aperture |
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*[[Field of view]] |
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[[Category: |
[[Category:Geometrical optics]] |
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[[Category:Angle]] |
[[Category:Angle]] |
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[[de:Öffnungswinkel]] |
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[[es:Apertura angular]] |
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[[it:Apertura angolare]] |
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[[nl:Openingshoek]] |
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[[zh:孔徑角]] |
Latest revision as of 05:57, 16 May 2021
![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Angular_aperture.svg/250px-Angular_aperture.svg.png)
The angular aperture of a lens is the angular size of the lens aperture as seen from the focal point:
where
- is the focal length
- is the diameter of the aperture.
Relation to numerical aperture
[edit]In a medium with an index of refraction close to 1, such as air, the angular aperture is approximately equal to twice the numerical aperture of the lens.[1]
Formally, the numerical aperture in air is:
In the paraxial approximation, with a small aperture, :
References
[edit]- ^ Albert Abraham Michelson (1995). Studies in Optics. Courier Dover. p. 32. ISBN 0-486-68700-7.
See also
[edit]- f-number
- Numerical aperture
- Acceptance angle, half the angular aperture
- Field of view