F-number

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Image:Aperture diagram.png In photography and optics, the f-number or focal ratio of an optical system expresses the diameter of the entrance pupil in terms of the effective focal length of the lens.

The f-number f/# is given by

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/#=f/16. The greater the f-number, the less light per unit area reaches the image plane of the system.

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).

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 pupil and aperture diameters by a factor of <math>\sqrt{2}</math>, and hence a halving of the area of the pupil. Image:Lens aperture side.jpg

Modern lenses use a standard f stops scale that corresponds to the sequence of the powers of <math>\sqrt{2}</math>: f/0.7, 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, f/64, f/90, f/128, etc. The values of the ratios are rounded off, to make them easy to write down.

The slash indicates division. For example, f/16 means that the pupil diameter is equal to the focal length divided by sixteen; that is, if the camera has an 80 mm lens, the light that reaches the film arrives through an opening that is 5 mm (80 mm/16) in diameter.

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. Opening up a lens by one stop allows twice as much light to fall on the film in a given period of time, therefore to have the same exposure, you must have a shutter speed twice as fast (shutter open half as long). Alternatively, you could use a film which is half as sensitive to light. This fundamental principle of photographic technique is known as reciprocity.

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. (The t in t-stop stands for transmission.)

On modern cameras, especially when aperture is set on the camera body, f-stops are often divided more finely, resulting in half stops or third stops. The latter system is more common, since it matches the ISO system of film speeds. For example, the aperture that is one third stop smaller than f/2.8 is f/3.2, two thirds smaller is f/3.5, and one whole stop smaller is f/4. The next few f-stops in this sequence are f/4.5, f/5, f/5.6, f/6.3, f/7.1, f/8, etc. In practice the maximum aperture of a lens may not be an integral power of <math>\sqrt{2}</math>, in which case it is usually a half or third stop above or below an integral power of <math>\sqrt{2}</math>.

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

Picture quality also varies with f-stop. The optimal f-stop varies with the lens characteristics. For 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 limitations of the lens design known as aberrations will dominate. The larger number of elements in modern lenses allow the designer to compensate for aberrations, allowing the lens to give good pictures at a lower f-stop. Light falloff is also sensitive to f-stop. Many wide-angle lenses will show a significant light falloff (vignetting) at the edges for large apertures.

Photojournalists have a saying, "f/8 and be there." People have interpreted the expression differently, but one meaning is that f/8 will give a good enough picture, and being on the scene is more important than worrying excessively about technical details.

As an example of the use of f-numbers, an approximately correct exposure will be obtained on a sunny day by using an aperture of f/16 and a shutter speed close to the reciprocal of the ISO speed of the film; thus, using ISO 100 film, an aperture of f/16 and a shutter speed of 1/125th of a second. This is called the "sunny f/16 rule".

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