Focal length

For the special case of a thin lens in air, a positive focal length is the distance over which initially collimated (parallel) rays are brought to a focus, or alternatively a negative focal length indicates how far in front of the lens a point source must be located to form a collimated beam.

In most photography and all telescopy, where the subject is essentially infinitely far away, longer focal length (lower optical power) leads to higher magnification and a narrower angle of view; conversely, shorter focal length or higher optical power is associated with lower magnification and a wider angle of view.

On the other hand, in applications such as microscopy in which magnification is achieved by bringing the object close to the lens, a shorter focal length (higher optical power) leads to higher magnification because the subject can be brought closer to the center of projection.

The focal length of such a lens is defined as the point at which the spreading beams of light meet when they are extended backwards.

For an optical system in a medium other than air or vacuum, the front and rear focal lengths are equal to the EFL times the refractive index of the medium in front of or behind the lens (n1 and n2 in the diagram above).

The historical usage was to define the "focal length" as the EFL times the index of refraction of the medium.

[2][4] For a system with different media on both sides, such as the human eye, the front and rear focal lengths are not equal to one another, and convention may dictate which one is called "the focal length" of the system.

Some modern authors avoid this ambiguity by instead defining "focal length" to be a synonym for EFL.

[1] The distinction between front/rear focal length and EFL is important for studying the human eye.

For the case of a lens of thickness d in air (n1 = n2 = 1), and surfaces with radii of curvature R1 and R2, the effective focal length f is given by the Lensmaker's equation:[5]

In the sign convention used here, the value of R1 will be positive if the first lens surface is convex, and negative if it is concave.

In the sign convention used in optical design, a concave mirror has negative radius of curvature, so

Camera lens focal lengths are usually specified in millimetres (mm), but some older lenses are marked in centimetres (cm) or inches.

Focal length (f) and field of view (FOV) of a lens are inversely proportional.

To render closer objects in sharp focus, the lens must be adjusted to increase the distance between the rear principal plane and the film, to put the film at the image plane.

The focal length of a lens determines the magnification at which it images distant objects.

[7] This model leads to the simple geometric model that photographers use for computing the angle of view of a camera; in this case, the angle of view depends only on the ratio of focal length to film size.

Due to the popularity of the 35 mm standard, camera–lens combinations are often described in terms of their 35 mm-equivalent focal length, that is, the focal length of a lens that would have the same angle of view, or field of view, if used on a full-frame 35 mm camera.

Use of a 35 mm-equivalent focal length is particularly common with digital cameras, which often use sensors smaller than 35 mm film, and so require correspondingly shorter focal lengths to achieve a given angle of view, by a factor known as the crop factor.

The optical power of a lens or curved mirror is a physical quantity equal to the reciprocal of the focal length, expressed in metres.

For example, a 2-dioptre lens brings parallel rays of light to focus at 1⁄2 metre.

A flat window has an optical power of zero dioptres, as it does not cause light to converge or diverge.

[10] The main benefit of using optical power rather than focal length is that the thin lens formula has the object distance, image distance, and focal length all as reciprocals.

Additionally, when relatively thin lenses are placed close together their powers approximately add.