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# Angular aperture

The angular aperture of a lens is the apparent angle of the lens aperture as seen from the focal point:

:$a = 2 arctan left\left( frac \left\{D/2\right\} \left\{f\right\} ight\right)$

where :$f$ is the focal length:$D$ 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. [citebook|title=Studies in Optics |author=Albert Abraham Michelson|year= 1995|publisher=Courier Dover|pages=32|id=ISBN 0486687007|url= http://books.google.com/books?id=m2tUZ4_8WGMC&pg=PA32&dq=%22Angular+aperture%22&as_brr=3&ei=y--9Rob9J5PM6AKqhLX6Dg&ie=ISO-8859-1&output=html&sig=5iQK7FL25va8a06vSbx_gTFOGLg]

Formally, the numerical aperture in air is:

:$mathrm\left\{NA\right\} = sin a/2 = sin arctan left\left( frac \left\{D\right\} \left\{2 f\right\} ight\right)$

In the paraxial approximation, with a small aperture,

:$mathrm\left\{NA\right\} approx a/2$

References

ee also

*f-number
*Numerical aperture

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