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Numerical aperture of a thin lens. Numerical aperture is not typically used in photography. Instead, the angular aperture of a lens (or an imaging mirror) is expressed by the f-number, written f /N, where N is the f-number given by the ratio of the focal length f to the diameter of the entrance pupil D: =.
The f-number N is given by: = where f is the focal length, and D is the diameter of the entrance pupil (effective aperture).It is customary to write f-numbers preceded by "f /", which forms a mathematical expression of the entrance pupil's diameter in terms of f and N. [1]
The angular aperture of a thin lens with focal point at F and an aperture of diameter ... is the focal length ... the numerical aperture in air is:
Here NA is the numerical aperture, is half the included angle of the lens, which depends on the diameter of the lens and its focal length, is the refractive index of the medium between the lens and the specimen, and is the wavelength of light illuminating or emanating from (in the case of fluorescence microscopy) the sample.
The f-number ("relative aperture"), N, is defined by N = f / E N, where f is the focal length and E N is the diameter of the entrance pupil. [2] Increasing the focal length of a lens (i.e., zooming in) will usually cause the f-number to increase, and the entrance pupil location to move further back along the optical axis.
A more typical consumer zoom will have a variable maximum relative aperture since it is harder and more expensive to keep the maximum relative aperture proportional to the focal length at long focal lengths; f /3.5 to f /5.6 is an example of a common variable aperture range in a consumer zoom lens.
Similarly, a point source of light placed at the focal point will produce a collimated beam emanating from the opposite side of the lens, and the lens's large ratio of diameter to focal length (large numerical aperture) allows more light to be captured than would be possible with other spherical lenses. This makes ball lenses particularly ...
The focal point F and focal length f of a positive (convex) lens, a negative (concave) lens, a concave mirror, and a convex mirror.. The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power.