Reciprocal length
Reciprocal length or inverse length is a quantity or measurement used in several branches of science and mathematics. As the reciprocal of length, common units used for this measurement include the reciprocal metre or inverse metre (symbol: m), the reciprocal centimetre or inverse centimetre (symbol: cm). Quantities measured in reciprocal length include: In optics, the dioptre is a unit equivalent to reciprocal metre. Measure of energy. 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, , is an energy unit equal to the energy of a photon with a wavelength of 1  cm. That energy amounts to approximately or . The energy is inversely proportional to the size of the unit of which the reciprocal is used, and inversely proportional to the number of reciprocal length units. In other words, the higher the quantity of inverse length, the lower the energy. For example, in terms of energy, one reciprocal metre equals (one hundredth) as much as a reciprocal centimetre. Five reciprocal metres are five times less energy, or one-fifth as much energy, as one reciprocal metre.