f-number

It is calculated by dividing the system's focal length by the diameter of the entrance pupil ("clear aperture").

[1][2][3] The f-number is also known as the focal ratio, f-ratio, or f-stop, and it is key in determining the depth of field, diffraction, and exposure of a photograph.

The numerical aperture takes into account the refractive index of the medium in which the system is working, while the f-number does not.

Ignoring differences in light transmission efficiency, a lens with a greater f-number projects darker images.

Opening up a lens by one stop allows twice as much light to fall on the film in a given period of time.

Aperture, shutter speed, and film sensitivity are linked: for constant scene brightness, doubling the aperture area (one stop), halving the shutter speed (doubling the time open), or using a film twice as sensitive, has the same effect on the exposed image.

For all practical purposes extreme accuracy is not required (mechanical shutter speeds were notoriously inaccurate as wear and lubrication varied, with no effect on exposure).

Ignoring the f-number markings, the f-stops make a logarithmic scale of exposure intensity.

Most twentieth-century cameras had a continuously variable aperture, using an iris diaphragm, with each full stop marked.

Steps of one-third stop (1⁄3 EV) are the most common, since this matches the ISO system of film speeds.

Doubling or halving the sensitivity is equal to a difference of one T-stop in terms of light transmittance.

Most electronic cameras allow the user to adjust the amplification of the signal coming from the image sensor.

Depth of field can be described as depending on just angle of view, subject distance, and entrance pupil diameter (as in von Rohr's method).

At small apertures, depth of field and aberrations are improved, but diffraction creates more spreading of the light, causing blur.

Many wide-angle lenses will show a significant light falloff (vignetting) at the edges for large apertures.

Practically, f/8 (in 35 mm and larger formats) allows adequate depth of field and sufficient lens speed for a decent base exposure in most daylight situations.

Typically, the pupil can dilate to be as large as 6–7 mm in darkness, which translates into the maximal physical aperture.

Treating the eye as an ordinary air-filled camera and lens results in an incorrect focal length and f-number.

In photography the focal ratio varies the focal-plane illuminance (or optical power per unit area in the image) and is used to control variables such as depth of field.

When using an optical telescope in astronomy, there is no depth of field issue, and the brightness of stellar point sources in terms of total optical power (not divided by area) is a function of absolute aperture area only, independent of focal length.

The f-number accurately describes the light-gathering ability of a lens only for objects an infinite distance away.

In photography this means that as one focuses closer, the lens's effective aperture becomes smaller, making the exposure darker.

In 1867, Sutton and Dawson defined "apertal ratio" as essentially the reciprocal of the modern f-number.

The terms 'apertal ratio' and 'focal range' have not come into general use, but it is very desirable that they should, in order to prevent ambiguity and circumlocution when treating of the properties of photographic lenses.

To ascertain this, divide the equivalent focus by the diameter of the actual working aperture of the lens in question; and note down the quotient as the denominator with 1, or unity, for the numerator.

Make a small round hole in the centre of the cardboard with a piercer, and now remove to a darkened room; apply a candle close to the hole, and observe the illuminated patch visible upon the front combination; the diameter of this circle, carefully measured, is the actual working aperture of the lens in question for the particular stop employed.

[24] According to an English review of his book, in 1894, "The necessity of clearly distinguishing between effective aperture and diameter of physical stop is strongly insisted upon.

[26] At the same time, there were a number of aperture numbering systems designed with the goal of making exposure times vary in direct or inverse proportion with the aperture, rather than with the square of the f-number or inverse square of the apertal ratio or intensity ratio.

But these systems all involved some arbitrary constant, as opposed to the simple ratio of focal length and diameter.

They show the hooked italic 'ƒ' not only in the symbol, but also in the term f-number, which today is more commonly set in an ordinary non-italic face.