Reciprocal lengthorinverse length is a quantityormeasurement used in several branches of science and mathematics, defined as the reciprocaloflength.
Common units used for this measurement include the reciprocal metreorinverse metre (symbol: m−1), the reciprocal centimetreorinverse centimetre (symbol: cm−1). In optics, the dioptre is a unit equivalent to reciprocal metre.
Quantities measured in reciprocal length include:
In some branches of physics, the universal constants c, the speed of light, and ħ, the reduced Planck constant, are treated as being unity (i.e. that c = ħ = 1), which leads to mass, energy, momentum, frequency and reciprocal length all having the same unit. As a result, reciprocal length is used as a measure of energy. The frequency of a photon yields a certain photon energy, according to the Planck–Einstein relation, and the frequency of a photon is related to its spatial frequency via the speed of light. Spatial frequency is a reciprocal length, which can thus be used as a measure of energy, usually of a particle. For example, the reciprocal centimetre, cm−1, is an energy unit equal to the energy of a photon with a wavelength of 1 cm. That energy amounts to approximately 1.24×10−4 eVor1.986×10−23 J.
The energy is inversely proportional to the size of the unit of which the reciprocal is used, and is proportional to the number of reciprocal length units. For example, in terms of energy, one reciprocal metre equals 10−2 (one hundredth) as much as a reciprocal centimetre. Five reciprocal metres are five times as much energy as one reciprocal metre.