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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>d</math>.|thumb|250px]]


The '''angular aperture''' of a [[lens (optics)|lens]] is the apparent [[angle]] 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>
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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= http://books.google.com/books?id=m2tUZ4_8WGMC&pg=PA32&dq=%22Angular+aperture%22&ie=ISO-8859-1&output=html}}</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
 
[[Category:Optics]]
[[Category:Angle]]

Latest revision as of 16:24, 5 January 2015


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