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# F-number

 Detail of a camera showing f stop scale.

In photography the f-number expresses the diameter of the diaphragm aperture in terms of the effective focal length of the lens. For example, f/16 represents a diaphragm aperture diameter that is one-sixteenth of the focal length.

The higher the f-number, the less light is admitted through the lens.

f stops are a way of representing a convenient sequence of f-numbers in a geometric progression. Each 'stop' is marked with its corresponding f-number, and represents a halving of the light intensity from the one before, corresponding to a decrease of the diaphragm aperture diameter by a factor of √2, and hence an halving of the area of the aperture.

Modern lenses use a standard f stops scale that corresponds to the sequence of the powers of √2 : f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, f/32, f/45 and f/64. (Note that the values of the ratios are rounded off, to make them easy to write down).

Shutter speeds are arranged in a similar scale, so that one step in the shutter speed scale corresponds to one step in the f stop scale.

Photographers sometimes express exposure ratios in terms of 'stops'. If we ignore the f-number markings, the f-stops make a logarithmic scale of exposure intensity. Given this interpretation, you can then think of taking a half-step along this scale, to make an exposure difference of "half a stop".

Since all lenses absorb some portion of the light passing through them (particularly zoom lenses containing many elements), for exposure purposes a T-stop is sometimes used instead of f-stop. The T-numbers are adjusted so that the amount of light transmitted through the lens at a given T-stop is equal to that going through an ideal non-absorbing lens set at that f-stop.

In practice the maximal aperture of a lens often differs from a power of √2, and is not one of the standard f-stops. For example, the sequence of F-stops on the lens depicted in the picture above has f-numbers of f/3.5, f/5.6, f/8, f/11, f/16 and f/22.

Depth of field increases with f-stop; for an example of this relationship, visit the depth of field article.

Picture sharpness also varies with f-stop. The optimal f-stop vary with the lens characteristics. For example, on modern standard lenses having 6 or 7 elements the sharpest image is obtained around f/5.6-f/8, while for older standard lenses having only 4 elements (Tessar formula) stopping to f/11 will give the sharpest image. The reason the sharpness is best at medium f-numbers is that the sharpness at high f-number is constrained by diffraction, whereas at low f-numbers lens faults known as aberrationss will dominate.

As an example of the use of f-numbers, an approximately correct exposure will be obtained on a sunny day using ISO 125 film, an aperture of f/16 and a shutter speed of 1/125th of a second. This is called the "sunny f/16 rule".

See also: