Editing Angular aperture (section)

== 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>