Editing Focal length (section)

== In photography ==
{{Multiple image |align=center |width=150 |image1=Angleofview 28mm f4.jpg |caption1=28&nbsp;mm lens |image2=Angleofview 50mm f4.jpg |caption2=50&nbsp;mm lens |image3=Angleofview 70mm f4.jpg |caption3=70&nbsp;mm lens |image4=Angleofview 210mm f4.jpg |caption4=210&nbsp;mm lens |footer=An example of how lens choice affects angle of view. The photos above were taken by a [[135 film|35&nbsp;mm]] camera at a fixed distance from the subject. |footer_align=center}}
[[File:Thin lens images.svg|thumb|upright=1.5|Images of black letters in a thin convex lens of focal length {{mvar|f}} are shown in red. Selected rays are shown for letters '''E''', '''I''' and '''K''' in blue, green and orange, respectively. '''E''' (at {{math|2''f''}}) has an equal-size, real and inverted image; '''I''' (at {{mvar|f}}) has its image at infinity; and '''K''' (at {{math|1={{Sfrac|''f''|2}}}}) has a double-size, virtual and upright image.]]
[[File:Camera focal length distance house animation.gif|thumb|upright=1.5|In this computer simulation, adjusting the field of view (by changing the focal length) while keeping the subject in frame (by changing accordingly the position of the camera) results in vastly differing images. At focal lengths approaching infinity (0 degrees of angle of view), the light rays are nearly parallel to each other, resulting in the subject looking "flattened". At small focal lengths (bigger field of view), the subject appears "foreshortened".]]

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

Focal length {{(--}}{{mvar|f}}{{--)}} and [[field of view]] (FOV) of a lens are inversely proportional. For a standard [[rectilinear lens]], <math display=inline>\mathrm{FOV} = 2\arctan{\left({x\over2f}\right)}</math>, where {{mvar|x}} is the width of the film or imaging sensor.

When a photographic lens is set to "infinity", its rear [[principal plane]] is separated from the sensor or film, which is then situated at the [[focal plane]], by the lens's focal length. Objects far away from the camera then produce sharp images on the sensor or film, which is also at the image plane.

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 {{mvar|f}}, the distance from the front principal plane to the object to photograph {{math|''s''{{sub|1}}}}, and the distance from the rear principal plane to the image plane {{math|''s''{{sub|2}}}} are then related by:

<math display=block>\frac{1}{s_1} + \frac{1}{s_2} = \frac{1}{f}\,.</math>

As {{math|''s''{{sub|1}}}} is decreased, {{math|''s''{{sub|2}}}} must be increased. For example, consider a [[normal lens]] for a [[35mm format|35&nbsp;mm]] camera with a focal length of {{math|1=''f'' {{=}}}} 50&nbsp;mm. To focus a distant object ({{math|1=''s''{{sub|1}} ≈ ∞}}), the rear principal plane of the lens must be located a distance {{math|1=''s''{{sub|2}} {{=}}}} 50&nbsp;mm from the film plane, so that it is at the location of the image plane. To focus an object 1&nbsp;m away ({{math|1=''s''{{sub|1}} {{=}}}} 1,000&nbsp;mm), the lens must be moved 2.6&nbsp;mm farther away from the film plane, to {{math|1=''s''{{sub|2}} {{=}}}} 52.6&nbsp;mm.

The focal length of a lens determines the magnification at which it images distant objects.  It is equal to the distance between the image plane and a [[pinhole camera|pinhole that images]] distant objects the same size as the lens in question.  For [[rectilinear lens]]es (that is, with no [[image distortion]]), the imaging of distant objects is well modelled as a [[pinhole camera model]].<ref>
{{cite book
 | title = Practical astrophotography
 | edition = 
 | first = Jeffrey | last = Charles
 | publisher = Springer
 | year = 2000
 | isbn = 978-1-85233-023-1
 | pages = [https://archive.org/details/practicalastroph00char/page/63 63]–66
 | url = https://archive.org/details/practicalastroph00char
 | url-access = registration
 }}</ref>  
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 format|film size]].  In general, the angle of view depends also on the distortion.<ref>
{{cite book
 | title = The Focal encyclopedia of photography
 | edition = 3rd
 | first1 = Leslie | last1 = Stroebel
 | first2 = Richard D. | last2 = Zakia
 | publisher = [[Focal Press]]
 | year = 1993
 | isbn = 978-0-240-51417-8
 | page = [https://archive.org/details/focalencyclopedi00lesl/page/27 27]
 | url = https://archive.org/details/focalencyclopedi00lesl
 | url-access = registration
 }}</ref>

A lens with a focal length about equal to the diagonal size of the film or sensor format is known as a [[normal lens]]; its angle of view is similar to the angle subtended by a large-enough print viewed at a typical viewing distance of the print diagonal, which therefore yields a normal perspective when viewing the print;<ref>
{{cite book
 | title = View Camera Technique
 | first = Leslie D. | last = Stroebel
 | publisher = [[Focal Press]]
 | year = 1999
 | pages = 135–138
 | isbn = 978-0-240-80345-6
 | url = https://books.google.com/books?id=71zxDuunAvMC&q=appear-normal+focal-length-lens+print-size+diagonal+viewer+distance&pg=PA136  
 }}</ref> 
this angle of view is about 53 degrees diagonally. For [[Full-frame digital SLR|full-frame]] 35&nbsp;mm-format cameras, the diagonal is 43&nbsp;mm and a typical "normal" lens has a 50&nbsp;mm focal length.  A lens with a focal length shorter than normal is often referred to as a [[wide-angle lens]] (typically 35&nbsp;mm and less, for 35&nbsp;mm-format cameras), while a lens significantly longer than normal may be referred to as a [[telephoto lens]] (typically 85&nbsp;mm and more, for 35&nbsp;mm-format cameras). Technically, long focal length lenses are only "telephoto" if the focal length is longer than the physical length of the lens, but the term is often used to describe any long focal length lens.

Due to the popularity of the [[135 film|35&nbsp;mm standard]], camera–lens combinations are often described in terms of their 35&nbsp;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&nbsp;mm camera.  Use of a 35&nbsp;mm-equivalent focal length is particularly common with [[digital camera]]s, which often use sensors smaller than 35&nbsp;mm film, and so require correspondingly shorter focal lengths to achieve a given angle of view, by a factor known as the [[crop factor]].