Notation
The f-number f/#, often notated as N, is given by
f/# = N = f/D
where f is the focal length, and D is the diameter of the entrance pupil. By convention, "f/#" is treated as a single symbol, and specific values of f/# are written by replacing the number sign with the value. For example, if the focal length is 16 times the pupil diameter, the f-number is f/16, or N = 16. The greater the f-number, the less light per unit area reaches the image plane of the system.
The literal interpretation of the f/N notation for f-number N is as an arithmetic expression for the effective aperture diameter (input pupil diameter), the focal length divided by the f-number: D = f / N.
The pupil diameter is proportional to the diameter of the aperture stop of the system. In a camera, this is typically the diaphragm aperture, which can be adjusted to vary the size of the pupil, and hence the amount of light that reaches the film or image sensor. Other types of optical system, such as telescopes and binoculars may have a fixed aperture, but the same principle holds: the greater the focal ratio, the fainter the images created (measuring brightness per unit area of the image). Note that the common assumption in photography that the pupil diameter is equal to the aperture diameter is not correct for all types of camera lens. A focal ratio of f/16 does not always mean that the physical aperture inside the camera lens has diameter equal to one sixteenth the focal length.
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