The **angular aperture** of a lens is the angular size of the lens aperture as seen from the focal point:

where

- is the focal length
- 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.^{[1]}

Formally, the numerical aperture in air is:

In the paraxial approximation, with a small aperture, :

## References

**^**Albert Abraham Michelson (1995).*Studies in Optics*. Courier Dover. p. 32. ISBN 0-486-68700-7.

## See also

- f-number
- Numerical aperture
- Acceptance angle, half the angular aperture
- Field of view