# Dioptre

A dioptre (British spelling) or diopter (American spelling) is a unit of measurement of the optical power of a lens or curved mirror, which is equal to the reciprocal of the focal length measured in metres. (1 dioptre = 1 m−1.) It is thus a unit of reciprocal length. For example, a 3-dioptre lens brings parallel rays of light to focus at ​13 metre. A flat window has an optical power of zero dioptres, and does not cause light to converge or diverge. Dioptres are also sometimes used for other reciprocals of distance, particularly radii of curvature and the vergence of optical beams.

The main benefit of using optical power rather than focal length is that the lensmaker's equation has the object distance, image distance, and focal length all as reciprocals. A further benefit is that when 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 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−1). However most languages have borrowed the original name and some national standardization bodies like DIN specify a unit name (dioptrie, dioptria, etc.) and derived unit symbol "dpt".

The idea of numbering lenses based on the reciprocal of their focal length in meters was first suggested by Nagel in 1866.[1][2] The term dioptre was proposed by French ophthalmologist Ferdinand Monoyer in 1872, based on earlier use of the term dioptrice by Johannes Kepler.[3][4][5]

## In vision correction

The fact that optical powers are approximately additive enables an eye care professional to prescribe corrective lenses 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). Optical power can also be used to adjust a basic prescription for reading. Thus an eye care professional, having determined that a myopic (nearsighted) 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 (ability to alter focus). This is the same as saying that −1 dioptre lenses are prescribed for reading.

In humans, the total optical power of the relaxed eye is approximately 60 dioptres.[6][7] The cornea accounts for approximately two-thirds of this refractive power (about 40 dioptres) and the crystalline lens contributes the remaining one-third (about 20 dioptres).[6] In focusing, the ciliary muscle contracts to reduce the tension or stress transferred to the lens by the 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 15 to 20 dioptres in the very young, decreasing to about 10 dioptres at age 25, and to around 1 dioptre above age 50.

Convex lenses 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. Concave lenses 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 reading glasses will be rated at +1.00 to +3.00 dioptres. Optometrists usually measure refractive error using lenses graded in steps of 0.25 dioptres.

## Curvature

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 will give approximately the right result, as long as the thickness of the lens is much less than the radius of curvature of one of the surfaces. For a mirror the optical power is φ = 2C.

## Relation to magnifying power

The magnifying power V of a simple magnifying glass is related to its optical power φ by

${\displaystyle V=0.25\ \mathrm {m} \times \varphi +1}$ .

This is approximately the magnification observed when a person with normal vision holds the magnifying glass close to his or her eye.

## References

1. ^ Rosenthal, J. William (1996). Spectacles and Other Vision Aids: A History and Guide to Collecting. Norman. p. 32. ISBN 9780930405717.
2. ^ Collins, Edward Treacher (1929). The history & traditions of the Moorfields Eye Hospital: one hundred years of ophthalmic discovery & development. London: H.K. Lewis. p. 116.
3. ^ Monoyer, F. (1872). "Sur l'introduction du système métrique dans le numérotage des verres de lunettes et sur le choix d'une unité de réfraction". Annales d'Oculistiques (in French). Paris. 68: 101.
4. ^ Thomas, C. "Monoyer, Ferdinand". La médecine à Nancy depuis 1872 (in French). Retrieved 2011-04-26.
5. ^ Colenbrander, August. "Measuring Vision and Vision Loss" (PDF). Smith-Kettlewell Institute. Retrieved 2009-07-10.
6. ^ a b Najjar, Dany. "Clinical optics and refraction". Eyeweb. Archived from the original on 2008-03-23. Retrieved 2008-03-25.
7. ^ Palanker, Daniel (October 28, 2013). "Optical Properties of the Eye". American Academy of Ophthalmology. Retrieved 2017-10-16.