From wikipedia:
In
optics, the
f-number (sometimes called
focal ratio,
f-ratio,
f-stop, or
relative aperture[SUP]
[1][/SUP]) of an optical system is the ratio of the
lens's focal length to the diameter of the
entrance pupil[SUP]
[2][/SUP]. It is a
dimensionless number that is a quantitative measure of
lens speed, an important concept in
photography.
The f-number is given by
where
is the
focal length, and
is the diameter of the entrance pupil (effective aperture). It is customary to write f-numbers preceded by
f/[SUP]
[3][/SUP], which forms a mathematical expression of the entrance pupil diameter in terms of
f (a symbol denoting the focal length), and the f-number. For example, if the focal length is 16 mm and the entrance pupil diameter is 1 mm, the f-number is 16 and the aperture would be expressed as
f/16. Ignoring differences in lens transmission efficiency, the greater the f-number, the darker the image projected by the lens. The amount of light transmitted from each object in the lens's field of view to each unit of area of the film (or sensor) decreases with the square of the f-number. Doubling the f-number decreases the exposure by a factor of four. To maintain the same exposure when doubling the f-number, the exposure time would need to be four times as long.
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. The common assumption in photography that the pupil diameter is
equal to the aperture diameter is not correct for many types of camera lens, because of the magnifying effect of lens elements in front of the aperture.
A 100 mm focal length lens with an aperture setting of
f/4 will have a pupil diameter of 25 mm. A 200 mm focal length lens with a setting of
f/4 will have a pupil diameter of 50 mm. The 200 mm lens's
f/4 opening is larger than that of the 100 mm lens but both will produce the same
illuminance in the focal plane when imaging an object of a given
luminance.
In other types of optical system, such as
telescopes and
binoculars, the same principle holds: the greater the focal ratio, the fainter the images created (measuring brightness per unit area of the image).