Editing Normal lens

{{short description|Type of photography and cinematography lens}}
{{Multiple issues|
{{more citations needed|date=April 2017}}
{{Cleanup rewrite|date=October 2022}}
}}
<!-- Deleted image removed: [[File:Demonstration of 'Normal' lens print superimposed on wider angle view of original scene for discussion of Normal lens.jpg|thumb|right|In his series ''FILMography'' Canadian photographer [[Christopher Moloney]] matches the perspective of scenes from movies (e.g., ''[[You've Got Mail]]'' ([[1998 in film|1998]])) with their real-life, present-day locations.]] -->In [[photography]] and [[cinematography]], a '''normal lens''' is a [[photographic lens|lens]] that reproduces a [[Angle of view|field of view]] that appears "natural" to a human observer. In contrast, depth compression and expansion with shorter or longer [[focal length]]s introduces noticeable, and sometimes disturbing, distortion.

== Mimicking human vision  ==
Photographic technology employs different physical methods from the human eye in order to capture images. Thus, manufacturing optics which produce images that appear natural to human vision is problematic.

The eye has a nominal focal length of approximately 17&nbsp;mm,<ref>Pocock, Gillian, Richards, Christopher D., and Richards, Dave A. (2013). ''Human physiology'' (4th ed). Oxford University Press, Oxford p214</ref> but it varies with [[Accommodation (eye)|accommodation]]. The nature of human binocular [[Visual perception|vision]], which uses two lenses instead of a single one, and post-processing by the cortex is very different from the process of making and rendering a photograph, video or film, and then looking at those.

The structure of the [[human eye]] has a concave [[retina]], rather than a flat sensor. This produces effects observed by [[Abraham Bosse]] who, in his 1665 illustration ''To prove that one can neither define nor paint as the eye sees'', demonstrated how the circular projection of the visual cone conflicts with the flat plane of the picture surface,<ref>{{Citation|author1=Abraham Bosse|title=Traité des pratiques geometrales et perspectives enseignées dans l'Academie royale de la peinture et sculpture|url=https://trove.nla.gov.au/work/35298327|date=1665|publisher=A Paris Chez l'auteur|access-date=28 July 2018|author2=Cellier, Antoine, 17th cent|author3=Académie royale de peinture et de sculpture (France)}}</ref> prompting continued debate over whether straight lines in the world are perceived as straight or curved in a form of [[Distortion (optics)|barrel distortion]], and whether they should be depicted as straight in the picture plane.<ref>Tyler, C.W. (2009) Editorial Essay: Straightness and the sphere of vision. ''Perception'' 38, pp. 1423–1427</ref>

[[Hermann von Helmholtz|Hermann von Helmholtz's]] [[Distortion (optics)|pin-cushioned]] chessboard figure demonstrates that straight lines in the world are not always perceived as straight and, conversely, that curved lines in the world can sometimes be seen as straight.<ref>Rogers, B., & Brecher, K. (2007). Straight Lines, 'Uncurved Lines', and Helmholtz's 'Great Circles on the Celestial Sphere'. ''Perception'', 36(9), 1275-1289.</ref> Furthermore, the retina has variable sensitivity across its wider-than-180° horizontal field of view, as well as differences in resolution between [[Peripheral vision|peripheral]] and [[foveal]] vision.<ref>Cooper, E., Piazza, E., and Banks, M. (2012). The perceptual basis of common photographic practice. ''Journal of Vision'', 12(5), 8.</ref>

Given these differences between human vision and camera lenses, explanations in photography texts to account for this discrepancy nevertheless tend to gloss over or merely restate the problem in terms of the observed phenomena, or claim that using 50&nbsp;mm lenses "approximates the angle of view and magnification of human vision",<ref>Modrak, R., and Anthes, B. (2011) ''Reframing photography'', New York:Routledge</ref> or that "the normal focal length for a given format most closely approximates human sight, and projects an image with the least distortion and compression of space from foreground to background",<ref>Belt, A. F. (2008) ''The elements of photography: Understanding and creating sophisticated images''. 2nd ed Burlington, MA:Focal Press</ref> or that "the perspective is correct and we are most comfortable with a picture captured with a 50-mm lens".<ref>Current, I. (1990) Best viewing distance for photographers. ''PSA Journal'', Sept, 16</ref>

== What is 'normal'? ==
A test of what is a normal lens then, is to find one that renders a printed (or otherwise displayed) photograph of a scene that when held at 'normal' viewing distance (usually arm's length) in front of the original scene and viewed with one eye, matches the real-world and the rendered perspective, though [[Maurice Henri Léonard Pirenne|Maurice Pirenne]] (in 1970) and others demonstrate that it is possible to see a scene made with any lens in normal perspective if one adjusts the viewing distance; but that range becomes impractically close for wide angle photographs or too lengthy for a telephoto, and it requires viewing it from a static point at the centre of perspective from which the image was made,<ref>Pirenne, Maurice Henri Leonard (1970). ''Optics, painting & photography''. University Press, Cambridge [England]</ref> supporting the observations of perspective paintings made by [[Leonardo da Vinci]].<ref>Da Vinci L. (1970) In Richter J. P. (Ed.) ''The literary works of Leonardo da Vinci'', London:Phaidon</ref>

== The image circle ==
A normal lens typically has an angle of view that is close to one [[radian]] (~57.296˚) of the optical system's [[image circle]].{{citation needed|date=July 2018}} For [[135 film|135]] format (24 x 36&nbsp;mm), with an [[Incircle and excircles of a triangle|escribed]] image circle diameter equal to the diagonal of the frame (43.266&nbsp;mm), the focal length that has an angle of one radian of the inscribed circle is 39.6&nbsp;mm; the focal length that has an angle of one radian of the horizontally-bound [[Incircle and excircles of a triangle|inscribed]] image circle, is 33&nbsp;mm; the focal length that has an angle of one radian of the vertically-bound inscribed circle, is 22&nbsp;mm. This correlates with the popularity of 35 and 24&nbsp;mm lenses, and the existence of 40&nbsp;mm lenses, albeit the latter in a more restrained offer. A 50&nbsp;mm lens has a vertical-bound inscribed circle angle of view of ~0.5 radians. A 70&nbsp;mm focal length has a horizontally-bound inscribed circle angle of view of ~0.5 radians. An 85&nbsp;mm lens has an enscribed (frame diagonal) circle angle of view of ~0.5 radians. Effectively, the 24, 35 and 40&nbsp;mm trio have a 1:2 relation to the 50, 70 and 85 trio of focal lengths. "Normal" lenses, those that cover one radian in at least one of their inscribed or escribed image circles, belong to the first group, with 35 and 40&nbsp;mm lenses closer to one radian than 50&nbsp;mm lenses.

== Perspective effects of short or long focal-length lenses ==
Lenses with longer or shorter [[focal length]]s produce an expanded or contracted field of view that appears to [[Perspective distortion (photography)|distort the perspective]] when viewed from a normal viewing distance.<ref>{{cite book
 | title = Creating World-Class Photography: How Any Photographer Can Create Technically Flawless Photographs
 | author = Ernst Wildi
 | publisher = Amherst Media, Inc
 | year = 2001
 | isbn = 978-1-58428-052-1
 | page = 44
 | url = https://books.google.com/books?id=kC6-vduaO3cC&pg=PA44
 }}</ref><ref name="stroebel">{{cite book
 | title = View camera technique
 | edition = 7th
 | author = Leslie D. Stroebel
 | publisher = Focal Press
 | year = 1999
 | isbn = 978-0-240-80345-6
 | pages = 135–140
 | url = https://books.google.com/books?id=71zxDuunAvMC&pg=PA135
 }}</ref> Lenses of shorter focal length are called ''[[wide-angle lens]]es'', while longer-focal-length lenses are referred to as [[long-focus lens]]es<ref>[https://books.google.com/books?id=sbdGeFem1zwC&dq=%22normal+lens%22+%22long+focus%22&pg=PA71 Bruce Warren, Photography, page 71]</ref> (with the most common of that type being the ''[[telephoto lens]]es''). Superimposing a wide-angle image print against the original scene would require holding it closer to the eye, while the telephoto image would need to be placed well into the depth of the photographed scene, or a tiny print to be held at arm's length, to match their perspectives.{{citation needed|date=April 2017}}

Such is the extent of distortions of perspective with these lenses that they may not be permitted as legal evidence.<ref>Hampton Dillinger (1997) 'Words Are Enough: The Troublesome Use of Photographs, Maps, and Other Images in Supreme Court Opinions'. In ''Harvard Law Review''  Vol. 110, No. 8 (Jun., 1997), pp. 1704-1753  The Harvard Law Review Association</ref>

The [[International Center of Photography|ICP]] ''Encyclopaedia of Photography'' notes that for legal purposes: <blockquote>"Judges will not admit a picture that seems to have been tampered with or that distorts any aspect of the scene [or does not render a normal perspective]...That is, the size relationships of objects in the photograph should be equivalent to what they actually are."<ref>International Center of Photography (1984). Encyclopedia of photography (1st ed). Crown Publishers, New York supra note 88, at p.208</ref></blockquote>

== 'Normal' lenses vary for different formats ==
For still photography, a lens with a focal length about equal to the diagonal size of the [[Photographic film|film]] or [[Image sensor|sensor]] format is considered to be a normal lens; its angle of view is similar to the angle [[Subtended angle|subtended]] by a large-enough print viewed at a typical viewing distance equal to the print diagonal;<ref name="stroebel" /> this angle of view is about 53° diagonally. For cinematography, where the image is larger relative to viewing distance, a wider lens with a focal length of roughly a quarter of the film or sensor diagonal is considered 'normal'. The term '''normal lens''' can also be used as a synonym for [[rectilinear lens]]. This is a completely different use of the term.{{citation needed|date=April 2017}}

==Typical normal focal lengths for different formats==

===Film still===
[[File:Normal Lenses 7253.jpg|thumb|Four "normal" lenses for the 35&nbsp;mm format.]]
Typical normal lenses for various [[film format]]s for photography are:{{citation needed|date=April 2017}}

{| class="wikitable"
|-
! Film format !! Image dimensions !! Image diagonal !! Normal lens focal length
|-
| 9.5&nbsp;mm [[Minox]]
| 8 × 11&nbsp;mm
| 13.6&nbsp;mm
| 15&nbsp;mm
|-
| Half-frame
| 24 × 18&nbsp;mm
| 30&nbsp;mm
| 30&nbsp;mm
|-
| [[Advanced Photo System|APS]] C
| 16.7 × 25.1&nbsp;mm
| 30.1&nbsp;mm
| 28&nbsp;mm, 30&nbsp;mm
|-
| [[135 film|135]], 35&nbsp;mm
| 24 × 36&nbsp;mm
| 43.3&nbsp;mm
| 40&nbsp;mm, 50&nbsp;mm, 55&nbsp;mm
|-
| [[120 film|120]]/[[220 film|220]], 6 × 4.5 (645)
| 56 × 42&nbsp;mm
| 71.8&nbsp;mm
| 75&nbsp;mm
|-
| 120/220, 6 × 6
| 56 × 56&nbsp;mm
| 79.2&nbsp;mm
| 80&nbsp;mm
|-
| 120/220, 6 × 7
| 56 × 68&nbsp;mm
| 88.1&nbsp;mm
| 90&nbsp;mm
|-
| 120/220, 6 × 9
| 56 × 84&nbsp;mm
| 101.0&nbsp;mm
| 105&nbsp;mm
|-
| 120/220, 6 × 12
| 56 × 112&nbsp;mm
| 125.0&nbsp;mm
| 120&nbsp;mm
|-
| 120/220, 6 x 17
| 56 x 168&nbsp;mm
| 177.1&nbsp;mm
| 180&nbsp;mm
|-
| [[large format]] 4 × 5 [[sheet film]]
| 93 × 118&nbsp;mm (image area)
| 150.2&nbsp;mm
| 150&nbsp;mm
|-
| large format 5 × 7 sheet film
| 120 × 170&nbsp;mm (image area)
| 208.0&nbsp;mm
| 210&nbsp;mm
|-
| large format 8 × 10 sheet film
| 194 × 245&nbsp;mm (image area)
| 312.5&nbsp;mm
| 300&nbsp;mm
|-
|}

For a [[135 film|35&nbsp;mm]] [[camera]] with a diagonal of 43&nbsp;mm, the most commonly used ''normal'' lens is 50&nbsp;mm, but focal lengths between about 40 and 58&nbsp;mm are also considered ''normal''. The 50&nbsp;mm focal length was chosen by [[Oskar Barnack]], the creator of the [[Leica Camera|Leica camera]].<ref>{{cite journal |last1=Rimmasch |first1=Paul |title=Lens Testing: Reassessing the 50 mm Rule |journal=Journal of Forensic Identification |date=July 2017 |volume=67 |issue=3 |pages=323–340}}</ref><ref>{{cite journal |last1=Li |first1=Xiang |last2=Liu |first2=Jianzheng |last3=Baron |first3=Jessica |last4=Luu |first4=Khoa |last5=Patterson |first5=Eric |title=Evaluating effects of focal length and viewing angle in a comparison of recent face landmark and alignment methods |journal=EURASIP Journal on Image and Video Processing |date=March 2021 |volume=2021 |issue=1 |doi=10.1186/s13640-021-00549-3|s2cid=232414675 |doi-access=free }}</ref>

Note that the angle of view also depends on the [[aspect ratio (image)|aspect ratio]]. For example, a "normal" lens on 35&nbsp;mm does not have the same view as a "normal" lens on [[645 film|645]].{{citation needed|date=April 2017}}

===Digital still===
{{Also|Image sensor format#Table of sensor formats and sizes}}
In [[digital photography]], many smaller sensor sizes are specified in terms such as 1" or 2/3".
These measurements do not correspond directly to dimensions of the sensor, but rather to dimensions of an equivalent [[Video camera tube#Size|video camera tube (VCT)]].
The normal lens focal length is roughly 2/3 of the video camera tube diameter.

{| class="wikitable"
|-
! Sensor type !! equiv. VCT diameter !! Image dimensions !! Image diagonal !! Normal lens focal length
|-
| 1/3.6"
| 7.1&nbsp;mm
| 3.0 × 4.0&nbsp;mm
| 5.0&nbsp;mm
| 5&nbsp;mm
|-
| 1/3.2"
| 7.9&nbsp;mm
| 3.4 × 4.5&nbsp;mm
| 5.7&nbsp;mm
| 5.7&nbsp;mm
|-
| 1/3"
| 8.5&nbsp;mm
| 3.6 × 4.8&nbsp;mm
| 6.0&nbsp;mm
| 6&nbsp;mm
|-
| 1/2.7"
| 9.4&nbsp;mm
| 4.0 × 5.4&nbsp;mm
| 6.7&nbsp;mm
| 6.7&nbsp;mm
|-
| 1/2.5"
| 10.2&nbsp;mm
| 4.3 × 5.8&nbsp;mm
| 7.2&nbsp;mm
| 7&nbsp;mm
|-
| 1/2"
| 12.7&nbsp;mm
| 4.8 × 6.4&nbsp;mm
| 8.0&nbsp;mm
| 8&nbsp;mm
|-
| 1/1.8"
| 14.1&nbsp;mm
| 5.3 × 7.2&nbsp;mm
| 8.9&nbsp;mm
| 9&nbsp;mm
|-
| 1/1.7"
| 14.9&nbsp;mm
| 5.7 × 7.6&nbsp;mm
| 9.5&nbsp;mm
| 9.5&nbsp;mm
|-
| 2/3"
| 16.9&nbsp;mm
| 6.6 × 8.8&nbsp;mm
| 11.0&nbsp;mm
| 11&nbsp;mm
|-
| 1"
| 25.4&nbsp;mm
| 9.6 × 12.8&nbsp;mm
| 16.0&nbsp;mm
| 16&nbsp;mm
|-
| [[Four Thirds system|Four Thirds]]<ref name = "Four Thirds">{{citation | url = http://www.four-thirds.org/en/about/standard.html | publisher = Four Thirds Consortium | title = The Four Thirds Standard | access-date = 2009-04-17 | year = 2008 | archive-url = https://web.archive.org/web/20090307060248/http://www.four-thirds.org/en/about/standard.html | archive-date = 2009-03-07 | url-status = dead }}</ref>
| 33.9&nbsp;mm
| 13 × 17.3&nbsp;mm<ref name = "Olympus">{{cite web | url = http://www.olympus-europa.com/consumer/dslr_7045.htm | archive-url=https://web.archive.org/web/20110927125844/http://www.olympus-europa.com/consumer/dslr_7045.htm | publisher = Olympus Europa | title = No more compromises: the Four Thirds standard | archive-date=2011-09-27 }}</ref>
| 21.63&nbsp;mm
| 22&nbsp;mm
|-
| 4/3"
| 33.9&nbsp;mm
| 13.5 × 18.0&nbsp;mm
| 22.5&nbsp;mm
| 23&nbsp;mm
|-
| APS-C
| 45.7&nbsp;mm
| 15.1 × 22.7&nbsp;mm
| 27.3&nbsp;mm
| 27&nbsp;mm
|-
| [[Nikon DX format|DX]]
| n/a
| 15.8 × 23.7&nbsp;mm
| 28.4&nbsp;mm
| 28&nbsp;mm
|-
| [[Full-frame digital SLR|FF]] (35&nbsp;mm film)
| n/a
| 24 × 36&nbsp;mm
| 43.3&nbsp;mm
|  50&nbsp;mm
|-
| (6 × 5&nbsp;cm)
| n/a
| 36.7 × 49.0&nbsp;mm
| 61.2&nbsp;mm
|
|}

===Cinema===
In [[cinematography]], a [[focal length]] roughly equivalent to twice the diagonal of the image projected within the [[camera]] is considered normal, since movies are typically viewed from a distance of about twice the screen diagonal.<ref>Anton Wilson, ''Anton Wilson's Cinema Workshop'', American Cinematographer, 2004 (Page 100) [https://books.google.com/books?id=18Ck5PZX_ZsC&dq=cinematography+normal-lens&pg=PA101 online].</ref>

{| class="wikitable"
|-
! Film format !! Image dimensions !! Image diagonal !! Normal lens focal length
|-
| [[8 mm film|Standard 8]]
| 3.7 × 4.9&nbsp;mm
| 6.11&nbsp;mm
| 12–15&nbsp;mm
|-
| [[8 mm film|Single-8]] (FUJI)
| 4.2 × 6.2&nbsp;mm
| 7.5&nbsp;mm
| 15–17&nbsp;mm
|-
| [[Super 8 mm film|Super-8]]
| 4.2 × 6.2&nbsp;mm
| 7.5&nbsp;mm
| 15–17&nbsp;mm
|-
| [[9.5 mm film|9.5&nbsp;mm]]
| 6.5 × 8.5&nbsp;mm
| 10.7&nbsp;mm
| 20&nbsp;mm
|-
| [[16 mm film|16&nbsp;mm]]
| 7.5 × 10.3&nbsp;mm
| 12.7&nbsp;mm
| 25&nbsp;mm
|-
| [[35mm movie film|35&nbsp;mm]]
| 18.0 × 24.0&nbsp;mm
| 30.0&nbsp;mm
| 60&nbsp;mm
|-
| [[35mm movie film|35&nbsp;mm]], sound
| 16.0 × 22.0&nbsp;mm
| 27.2&nbsp;mm
| 50&nbsp;mm
|-
| [[65 mm film|65&nbsp;mm]]
| 52.6 × 23.0&nbsp;mm
| 57.4&nbsp;mm
| 125&nbsp;mm
|-
|}

==See also==
*[[Optics]]
*[[Distortion (optics)|Distortion]]
*[[Perception]]
*[[Visual perception]]
*[[Optical lens design|Lens design]]

==References==
{{reflist}}

[[Category:Photographic lenses]]
[[Category:Perspective projection]]
[[Category:Imaging]]