Angle of view

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In photography, angle of view (also referred to as field of view) is the extent of a given scene that is imaged onto the film or, in digital photography, the image sensor of a camera; that is, there is generally much more to a scene visible to humans than shows up in photos, and lenses of different focal lengths facilitate the recordation of different portions of that total scene.

The angle of view of a camera is a function of three parameters:

The dimensions of the frame, or format, defining the image size at the recording surface of a camera's film or the dimensions of the image sensor in digital cameras;
The focal length of the lens creating the image; and
The kind and degree of distortion of the lens.

It follows that for lenses producing rectilinear images,<ref>That is, a non-distorting and, therefore, non-fisheye lenses.</ref> the format dimensions completely define the angle of view for any given lens focal length. These are usually calculated three ways:

horizontally
diagonally (most common in photography)
vertically

For a lens producing a rectilinear image, the angle of view (α) can be calculated from the chosen dimension (d), and effective focal length (ƒ)<ref>Calculations for lenses producing non-rectilinear images are much more complex and in the end not very useful in most practical applications.</ref> thus:

<math>\alpha = 2 \arctan \frac {d} {2 f}</math> <ref>Because this is a trigonometric function, the angle of view does not vary linearly with the focal length. That is why a small change in the focal length of wide angle lenses produces a greater change in the angle of view than the same change would produce in a telephoto lens.</ref>

Note that the effective focal length can simply be set equal to the stated focal length of the lens (F), except in macro photography where the magnification factor (m) must be taken into account:

If the chosen dimension is to be the diagonal, then it can be calculated from the horizontal and vertical dimensions of the format through the use of the Pythagorean Theorem:

where h is the horizontal dimension of the image format and v is its vertical dimension. For example, the diagonal measurement of the image format for a full-frame 35 mm camera is:

Lenses are often referred to by terms that express their angle of view:

Ultra wide-angle lenses, also known as fisheye lenses, cover up to 180° (or even wider in special cases)
Wide-angle lenses generally cover between 100° and 60°
Standard lenses generally cover between 50° and 25°
Telephoto lenses generally cover between 15° and 10°
Super Telephoto lenses generally cover between 8° through less than 1°

Zoom lenses are a special case wherein the focal length, and hence angle of view, of the lens can be altered mechanically without removing the lens from the camera.

Longer lenses magnify the subject more, apparently compressing distance and (when focused on the foreground) blurring the background because of their shallower depth of field. Wider lenses tend to magnify distance between objects while allowing greater depth of field. Another result of using a wide angle lens is a greater apparent perspective distortion when the camera is not aligned perpendicularly to the subject: parallel lines converge at the same rate as with a normal lens, but converge more due to the wider total field. For example, buildings appear to be falling backwards much more severely when the camera is pointed upward from ground level than they would if photographed with a normal lens at the same distance from the subject, because more of the subject building is visible in the wide-angle shot.

Because different lenses generally require a different camera–subject distance to preserve the size of a subject, changing the angle of view can indirectly distort perspective, changing the apparent relative size of the subject and foreground.

*An example of how lens choice affects angle of view. 'The photos below were taken by a 35 mm camera.*
28 mm lens	50 mm lens
70 mm lens	210 mm lens

Note that the angle of view of a given lens is frequently, and incorrectly, referred to as the angle of coverage; a term which describes the properties of the image projected by the lens onto the focal plane. This confusion is not normally an issue with 135 film systems, such as single lens reflex cameras, as the relationship between the lens itself and the film size is almost always fixed. With a view camera, however, the photographer is permitted complete control over the lens–film relationship as well as the lens–subject relationship and thus the two factors come into play.

A circular fisheye lens, as opposed to a full-frame fisheye, is an example of a lens where the angle of coverage has been narrowed relative to the other lenses in that system. In many cases the angle of view of the circular fisheye will be almost exactly the same as the nearest full-frame fisheye; however, the image projected onto the film is rendered circular because the diameter of the image projected is narrower than that needed to cover the widest portion of the film.

[edit] Common lens angles of view

This table shows the diagonal, horizontal, and vertical angles of view, in degrees, for lenses producing rectilinear images used with 24×36 mm format (that is, 135 film or full-frame 35mm digital<ref>However, most interchangeable lens digital cameras do not use 24x36 mm photosensors and therefore produce narrower angles of view than set out in the table. See subtopic Digital camera issues in the article on wide-angle lenses for further discussion.</ref>)

Focal Length (mm)	13	15	18	21	24	28	35	50	85	105	135	180	210	300	400	500	600	830	1200
Diagonal (°)	118	111	100	91.7	84.1	75.4	63.4	46.8	28.6	23.3	18.2	13.7	11.8	8.25	6.19	4.96	4.13	2.99	2.07
Vertical (°)	85.4	77.3	67.4	59.5	53.1	46.4	37.8	27.0	16.1	13.0	10.2	7.63	6.54	4.58	3.44	2.75	2.29	1.66	1.15
Horizontal (°)	108	100.4	90.0	81.2	73.7	65.5	54.4	39.6	23.9	19.5	15.2	11.4	9.80	6.87	5.15	4.12	3.44	2.48	1.72