Diopters
A dioptre (uk), or diopter (us), 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 (that is, 1/metres). It is thus a unit of reciprocal length. For example, a 3-dioptre lens brings parallel rays of light to focus at 1⁄3 metre. A flat window has an optical power of zero dioptres, and does not converge or diverge light.
Dioptres are also sometimes used for other reciprocals of distance, particularly radii of curvature and the vergence of optical beams. The usage was proposed by French ophthalmologist Ferdinand Monoyer in 1872, based on earlier use of the term dioptrice by Johannes Kepler.
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-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.
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−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".
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