diopter (1/m)
Optical powerexact by definition
The dioptre is the unit of optical power, defined as the reciprocal of the focal length in metres. A lens of one dioptre brings parallel light to a focus one metre away, and a lens of two dioptres at half a metre. The relation is exact by definition, being nothing more than the reciprocal of a length in SI units.
Watch out: Positive dioptres describe converging lenses used to correct farsightedness, negative dioptres diverging lenses for nearsightedness. A prescription also carries a cylinder value in dioptres with an axis in degrees for astigmatism, and the sphere and cylinder are not interchangeable.
| 1 dpt | 1 dpt |
Proposed by the French ophthalmologist Ferdinand Monoyer in 1872 and adopted quickly by optometry, because the reciprocal form lets thin lenses in contact be added by simple arithmetic.
About the diopter (1/m)
The reason optometry uses reciprocal metres rather than focal lengths is additivity. Optical power adds where focal length does not: put a \(+2.00\) D lens against a \(+0.50\) D lens and you get \(+2.50\) D, whereas combining a 500 mm and a 2000 mm focal length requires \(1/f = 1/f_1 + 1/f_2\) every time. The whole apparatus of a phoropter, where the examiner flips lenses in and out of the light path, depends on that arithmetic being trivial.
The numbers map onto ordinary experience directly. A \(+2.00\) D pair of reading glasses focuses at \(1/2.00 = 0.5\) m, which is about where a book sits, and that is roughly the correction a typical person needs in their mid fifties as the natural lens stiffens. A \(-4.00\) D myopic eye focuses at 0.25 m unaided, meaning anything past 25 cm is blurred without correction. Contact lens and spectacle prescriptions differ slightly for strong corrections because the lens sits at a different distance from the eye, an effect called vertex distance that becomes significant past about four dioptres.