Editing Angular aperture

[[Image:Angular aperture.svg|right|The angular aperture <math>a</math> of a [[thin lens]] with focal point at '''''F''''' and an aperture of diameter <math>D</math>.|thumb|250px]]

The '''angular aperture''' <math>a</math> of a [[lens (optics)|lens]] is the [[angular size]] of the lens [[aperture]] as seen from the [[Focus (optics)|focal point]]:

:<math>a = 2 \arctan \left( \frac {D/2} {f} \right) = 2 \arctan \left( \frac {D} {2f} \right)</math>

where 
:<math>f</math> is the [[focal length]]
:<math>D</math> is the [[diameter]] of the [[aperture]].

== Relation to numerical aperture ==

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>

Formally, the numerical aperture in air is:

:<math>\mathrm{NA} = \sin a/2 = \sin \arctan \left( \frac {D} {2 f} \right)</math>

In the [[paraxial approximation]], with a small aperture, <math>D<f</math>:

:<math>\mathrm{NA} \approx a/2</math>

==References==
{{reflist}}

==See also==
*[[f-number]]
*[[Numerical aperture]]
*Acceptance angle, half the angular aperture
*[[Field of view]]

[[Category:Geometrical optics]]
[[Category:Angle]]