## All you need to know about F-Stop

The **f-number** of an optical system such as a camera lens is the ratio of the system’s focal length to the diameter of the entrance pupil. It is a dimensionless number that is a quantitative measure of lens speed, and an important concept in photography. It is also known as the **focal ratio**, **f-ratio**, or **f-stop**. It is the reciprocal of the **relative aperture**. The f-number is commonly indicated using a hooked f with the format f/N, where N is the f-number.

The f-number *N* or f# is given by:

where {\displaystyle f} is the focal length, and {\displaystyle 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 diameter in terms of f and *N*.^{[1]} For example, if a lens’s focal length is 10 mm and its entrance pupil diameter is 5 mm, the f-number is 2, expressed by writing “f/2”, and the aperture diameter is equal to {\displaystyle f/2}, where {\displaystyle f} is the focal length.

Ignoring differences in light transmission efficiency, a lens with a greater f-number projects darker images. The brightness of the projected image (illuminance) relative to the brightness of the scene in the lens’s field of view (luminance) decreases with the square of the f-number. Doubling the f-number decreases the relative brightness by a factor of four. To maintain the same photographic exposure when doubling the f-number, the exposure time would need to be four times as long.

Most lenses have an adjustable diaphragm, which changes the size of the aperture stop and thus the entrance pupil size. The entrance pupil diameter is not necessarily equal to the aperture stop diameter, because of the magnifying effect of lens elements in front of the aperture.

A 100 mm focal length f/4 lens has an entrance pupil diameter of 25 mm. A 200 mm focal length f/4 lens has an entrance pupil diameter of 50 mm. The 200 mm lens’s entrance pupil has four times the area of the 100 mm lens’s entrance pupil, and thus collects four times as much light from each object in the lens’s field of view. But compared to the 100 mm lens, the 200 mm lens projects an image of each object twice as high and twice as wide, covering four times the area, and so both lenses produce the same illuminance at the focal plane when imaging a scene of a given luminance.

A T-stop is an f-number adjusted to account for light transmission efficiency.

### Fractional stops

Most old cameras had a continuously variable aperture scale, with each full stop marked. Click-stopped aperture came into common use in the 1960s; the aperture scale usually had a click stop at every whole and half stop.

On modern cameras, especially when aperture is set on the camera body, f-number is often divided more finely than steps of one stop. Steps of one-third stop (1/3 EV) are the most common, since this matches the ISO system of film speeds. Half-stop steps are used on some cameras. Usually the full stops are marked, and the intermediate positions are clicked. As an 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.

To calculate the steps in a full stop (1 EV) one could use

- 2
^{0×0.5}, 2^{1×0.5}, 2^{2×0.5}, 2^{3×0.5}, 2^{4×0.5}etc.

The steps in a half stop (1/2 EV) series would be

- 2
^{0/2×0.5}, 2^{1/2×0.5}, 2^{2/2×0.5}, 2^{3/2×0.5}, 2^{4/2×0.5}etc.

The steps in a third stop (1/3 EV) series would be

- 2
^{0/3×0.5}, 2^{1/3×0.5}, 2^{2/3×0.5}, 2^{3/3×0.5}, 2^{4/3×0.5}etc.

As in the earlier DIN and ASA film-speed standards, the ISO speed is defined only in one-third stop increments, and shutter speeds of digital cameras are commonly on the same scale in reciprocal seconds. A portion of the ISO range is the sequence

- … 16/13°, 20/14°, 25/15°, 32/16°, 40/17°, 50/18°, 64/19°, 80/20°, 100/21°, 125/22°…

while shutter speeds in reciprocal seconds have a few conventional differences in their numbers (1/15, 1/30, and 1/60 second instead of 1/16, 1/32, and 1/64).

In practice the maximum aperture of a lens is often not an integral power of {\displaystyle \scriptstyle {\sqrt {2}}} (i.e., {\displaystyle \scriptstyle {\sqrt {2}}} to the power of a whole number), in which case it is usually a half or third stop above or below an integral power of {\displaystyle \scriptstyle {\sqrt {2}}}.

Modern electronically controlled interchangeable lenses, such as those used for SLR cameras, have f-stops specified internally in 1/8-stop increments, so the cameras’ 1/3-stop settings are approximated by the nearest 1/8-stop setting in the lens.

Source: Wikipedia