[[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 is the angular size of the lens aperture as seen from the 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