Editing Dioptre

{{short description|Unit of measurement of optical power}}
{{about|the unit of measure in optics||Diopter (disambiguation)}}
{{Use British English|date=October 2023}}
{{Infobox unit
| name          = dioptre
| quantity      = optical power
| standard      = <!--Not standardized-->
| symbol        = dpt
| symbol2       = D
| units1        = SI units
| inunits1      = 1 m<sup>−1</sup>
}}
[[File:optical_power_of_a_lens.svg|thumb|Illustration of the relationship between optical power in dioptres and focal length in metres.]]
A '''dioptre''' ([[British spelling]]) or '''{{lang|en-US|diopter}}''' ([[American spelling]]), symbol '''dpt''' or '''D''', is a [[unit of measurement]] with [[Dimension (physics)|dimension]] of [[reciprocal length]], equivalent to one [[reciprocal metre]], {{nowrap|1 dpt {{=}} 1 m<sup>−1</sup>}}. It is normally used to express the [[optical power]] of a [[lens (optics)|lens]] or curved [[mirror]], which is a [[physical quantity]] equal to the [[Multiplicative inverse|reciprocal]] of the [[focal length]], expressed in [[metre]]s. For example, a 3-dioptre lens brings parallel [[ray (optics)|rays]] of light to focus at {{frac|3}} metre. A flat window has an optical power of zero dioptres, as it does not cause light to converge or diverge. Dioptres are also sometimes used for other reciprocals of distance, particularly [[Radius of curvature (optics)|radii of curvature]] and the [[vergence (optics)|vergence]] of [[Optical beam|optical beams]].

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 [[thin lens|relatively thin lenses]] are placed close together their powers approximately add. Thus, a thin 2.0-dioptre lens placed close to a thin 0.5-dioptre lens yields almost the same focal length as a single 2.5-dioptre lens.

Though the dioptre is based on the [[International System of Units|SI]]-[[metric system]], it has not been included in the standard, so that there is no international name or symbol for this unit of measurement – within the [[international system of units]], this unit for optical power would need to be specified explicitly as the [[inverse metre]] (m<sup>−1</sup>). However most languages have borrowed the original name and some national standardization bodies like [[Deutsches Institut für Normung|DIN]] specify a unit name (dioptrie, dioptria, etc.). In [[vision care]] the symbol '''D''' is frequently used.

The idea of numbering lenses based on the reciprocal of their focal length in metres was first suggested by Albrecht Nagel in 1866.<ref>{{Cite book |title=Spectacles and Other Vision Aids: A History and Guide to Collecting |last=Rosenthal |first=J. William |date=1996 |publisher=Norman |isbn=9780930405717 |pages=32}}</ref><ref>{{Cite book |url=https://ucl-new-primo.hosted.exlibrisgroup.com/primo-explore/fulldisplay?vid=UCL_VU2&id=990011065180204761&inst=44UCL_INST&context=L |title=The history & traditions of the Moorfields Eye Hospital: one hundred years of ophthalmic discovery & development |last=Collins |first=Edward Treacher |publisher=[[H. K. Lewis & Co. Ltd.]] |year=1929 |location=London |pages=116}}</ref> The term ''dioptre'' was proposed by French [[ophthalmologist]] [[Ferdinand Monoyer]] in 1872, based on earlier use of the term ''[[dioptrice]]'' by [[Johannes Kepler]].<ref>{{cite journal | title=Sur l'introduction du système métrique dans le numérotage des verres de lunettes et sur le choix d'une unité de réfraction | last=Monoyer | first=F. | journal=Annales d'Oculistiques | year=1872 | volume=68 | location=Paris | page=101 | language=fr}}</ref><ref>{{cite web | url=http://www.professeurs-medecine-nancy.fr/Monoyer_C.htm | title=Monoyer, Ferdinand | work=La médecine à Nancy depuis 1872 | access-date=2011-04-26 | author=Thomas, C. | language=fr}}</ref><ref>{{cite web|last=Colenbrander|first=August|title=Measuring Vision and Vision Loss|url=http://www.ski.org/Colenbrander/Images/Measuring_Vis_Duane01.pdf|publisher=[[Smith-Kettlewell Institute]]|access-date=2009-07-10|archive-url=https://web.archive.org/web/20141204193231/http://www.ski.org/Colenbrander/Images/Measuring_Vis_Duane01.pdf|archive-date=2014-12-04|url-status=dead}}</ref>

==In vision correction==
The fact that optical powers are approximately [[wiktionary:additive|additive]] enables an [[eye care professional]] to prescribe [[corrective lens]]es as a simple correction to the [[eye|eye's]] optical power, rather than doing a detailed analysis of the entire optical system (the eye and the lens). Optical power can also be used to adjust a basic [[Eyeglass prescription|prescription]] for reading. Thus an eye care professional, having determined that a [[myopia|myopic]] (nearsighted) person requires a basic correction of, say, −2&nbsp;dioptres to restore normal distance vision, might then make a further prescription of 'add 1' for reading, to make up for lack of [[Accommodation (eye)|accommodation]] (ability to alter focus). This is the same as saying that −1&nbsp;dioptre lenses are prescribed for reading.

In humans, the total optical power of the relaxed eye is approximately 60 dioptres.<ref name=Najjar1>{{cite web |last=Najjar |first=Dany |url=http://www.eyeweb.org/optics.htm |title=Clinical optics and refraction |publisher=Eyeweb |access-date=2008-03-25 |url-status=dead |archive-url=https://web.archive.org/web/20080323035251/http://www.eyeweb.org/optics.htm |archive-date=2008-03-23 }}</ref><ref>{{cite web |url=https://www.aao.org/munnerlyn-laser-surgery-center/optical-properties-of-eye |title=Optical Properties of the Eye |publisher=American Academy of Ophthalmology |first=Daniel |last=Palanker |date=October 28, 2013 |access-date=2017-10-16}}</ref> The [[cornea]] accounts for approximately two-thirds of this refractive power (about 40 dioptres) and the [[lens (anatomy)|crystalline lens]] contributes the remaining one-third (about 20 dioptres).<ref name = Najjar1/> In focusing, the [[ciliary muscle]] contracts to reduce the [[Tension (mechanics)|tension]] or [[Stress (physics)|stress]] transferred to the lens by the [[Suspensory ligament of the lens|suspensory ligaments]]. This results in increased convexity of the lens which in turn increases the optical power of the eye. The [[amplitude of accommodation]] is about 11 to 16&nbsp;dioptres at age 15, decreasing to about 10&nbsp;dioptres at age 25, and to around 1&nbsp;dioptre above age 60.

[[Lens (optics)#Types of simple lenses|Convex lens]]es have positive dioptric value and are generally used to correct [[hyperopia]] (farsightedness) or to allow people with [[presbyopia]] (the limited accommodation of advancing age) to read at close range. [[over-the-counter drug|Over the counter]] [[eyeglasses|reading glasses]] are rated at +1.00 to +4.00&nbsp;dioptres. [[Lens (optics)#Types of simple lenses|Concave lens]]es have negative dioptric value and generally correct [[myopia]] (nearsightedness). Typical glasses for mild myopia have a power of −0.50 to −3.00&nbsp;dioptres. [[Optometrist]]s usually measure [[refractive error]] using lenses graded in steps of 0.25&nbsp;dioptres.

==Curvature==
{{Unreferenced section|date=January 2015}}
The dioptre can also be used as a measurement of [[curvature]] equal to the reciprocal of the [[radius]] measured in metres. For example, a [[circle]] with a radius of 1/2 metre has a curvature of 2 dioptres. If the curvature of a surface of a lens is ''C'' and the [[index of refraction]] is ''n'', the optical power is φ = (''n'' − 1)''C''. If both surfaces of the lens are curved, consider their curvatures as positive toward the lens and add them. This gives approximately the right result, as long as the thickness of the lens is much less than the [[radius of curvature (optics)|radius of curvature]] of one of the surfaces. For a [[mirror]] the optical power is φ = 2''C''.

==Relation to magnifying power==
{{further|Magnification|Magnifying glass#Magnification}}
The ''magnifying power'' {{mvar|V}} of a simple [[magnifying glass]] is related to its optical power {{mvar|φ}} by
:<math>V = 0.25\ \mathrm{m} \times \varphi + 1</math>.
This is approximately the magnification observed when a person with normal vision holds the magnifying glass close to his or her eye.

==See also==
*[[Astigmatism (optical systems)|Astigmatism]]
* [[Dioptrics]]
*[[Lens clock]]
*[[Lensmeter]]
*[[Optics]]
*[[Optometry]]
*{{section link|Prism correction|Prism dioptres}}
*[[Vertometer]]

==References==
{{reflist}}
{{refbegin}}
*{{cite book|first= John E|last= Greivenkamp|year= 2004|title= Field Guide to Geometrical Optics|publisher= [[SPIE#SPIE Press|SPIE]]|location= Bellingham, Wash|series= SPIE Field Guides vol. FG01|isbn= 978-0-8194-5294-8|oclc= 53896720}}
*{{cite book |first1= Eugene|last1= Hecht|first2= Zając|last2= Alfred|year= 1987|title= Optics|edition= 2nd|publisher= [[Addison–Wesley]]|location= Reading, Mass|isbn= 978-0-201-11609-0|oclc= 13761389}}
{{refend}}

[[Category:Optics]]
[[Category:Units of measurement]]
[[Category:Non-SI metric units]]