Dioptre
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Keilana
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Reverted edits by [[Special:Contributions/121.1.51.186|121.1.51.186]] to last version by Keilana (using [[WP:HG|Huggle]])
{{This|the unit of measure in optics|Diopter (disambiguation)}}
A '''dioptre''', or '''diopter''', is a [[unit of measurement]] of the [[optical power]] of a [[lens (optics)|lens]] or curved [[mirror]], which is equal to the [[Multiplicative inverse|reciprocal]] of the [[focal length]] measured in [[metre]]s (that is, 1/metres). For example, a 3 dioptre lens brings parallel [[ray (optics)|rays]] of light to focus at 1/3 metre. The same unit is also sometimes used for other reciprocals of distance, particularly [[Radius of curvature (optics)|radii of curvature]] and the [[vergence (optics)|vergence]] of optical beams. The term was proposed by French [[ophthalmologist]] Felix Monoyer in 1872.<ref>Monoyer F., ''Annales d'Oculistiques'' (Paris) 68:101 (1872)—proposed diopter notation. The term was coined by [[Johannes Kepler]] and was used for the title of his book ''[[Johannes Kepler#Dioptrice, the Somnium manuscript, and other work|Dioptrice]]'', in which he laid out some fundamental concepts on geometric optics.</ref><ref>[http://www.ski.org/Colenbrander/Images/Measuring_Vis_Duane01.pdf Colenbrander, August, ''Measuring Vision and Vision Loss''] pdf</ref>
Though the dioptre is based on the SI-[[metric system]] it has not been included in the standard so that there is no international name or abbreviation 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, ..) and derived unit symbol "dpt".
Quantifying a lens in terms of its optical power rather than its focal length is useful because when relatively thin lenses are placed close together their powers approximately add (see [[thin lens equation]]). Thus a thin 2-dioptre lens placed close to a thin 0.5-dioptre lens yields almost the same focal length as a 2.5-dioptre lens would have. This approximation enables an [[optometrist]] to prescribe [[corrective lens]]es as a simple correction to the eye's optical power, rather than doing a detailed analysis of the entire optical system (the eye and the lens).
Since optical power is approximately [[wiktionary:additive|additive]], it can also be used to adjust a basic prescription for reading. Thus an optometrist, having determined that a [[myopia|myopic]] person requires a basic correction of, say, −2 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 dioptre lenses are prescribed for reading.
In humans, the total convergence power of the relaxed eye is approximately 60 dioptres. The [[cornea]] accounts for approximately two-thirds of this refractive power and the [[lens (anatomy)|crystalline lens]] contributes the remaining third.<ref>{{cite web |last=Najjar |first=Dany |url=http://www.eyeweb.org/optics.htm |title=Clinical optics and refraction |accessdate=2008-03-25}}</ref> 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. As humans age, the [[amplitude of accommodation]] reduces from approximately 15 to 20 dioptres in the very young, to about 10 dioptres at age 25, to around 1 dioptre at 50 and over.
[[Lens (optics)#Types of 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. [[Lens (optics)#Types of lenses|Concave lens]]es have negative dioptric value and generally correct [[myopia]] (nearsightedness). Typical glasses for mild myopia will have a power of −1.00 to −3.00 dioptres, while [[over-the-counter drug|over the counter]] [[eyeglasses|reading glasses]] will be rated at +1.00 to +3.00 dioptres. [[Optometrist]]s usually measure [[refractive error]] using lenses graded in steps of 0.25 dioptres.
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 focusing power is ɸ = (''n'' − 1)''C''. If both surfaces of the lens are curved, consider their curvatures as positive toward the lens and add them. This will give 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 focusing power is ɸ = 2''C''.
==Relation to magnifying power==
The ''magnifying power'' of a simple magnifier is related to its optical power. This is covered in detail in the articles on [[magnification]] and [[Magnifying glass#Magnification|magnifying glass]]es.
==See also==
*[[Astigmatism]]
*[[Eyeglasses prescription]]
*[[Corrective lens]]
*[[Lens clock]]
*[[Lensmeter]]
*[[Optical power]]
*[[Optics]]
*[[Optometry]]
*[[Refractive error]]
==References==
{{reflist}}
*{{cite book | first=John E. | last=Greivenkamp | year=2004 | title=Field Guide to Geometrical Optics | publisher=SPIE | others=SPIE Field Guides vol. '''FG01''' | id=ISBN 0-8194-5294-7 }}
*{{cite book | first=Eugene|last=Hecht|year=1987|title=Optics|edition=2nd ed.|publisher=Addison Wesley|id=ISBN 0-201-11609-X}}
[[Category:Optics]]
[[Category:Units of measure]]
[[Category:Non-SI metric units]]
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