Reciprocal length or inverse length is a quantity or measurement used in several branches of science and mathematics, defined as the reciprocal of length.
Common units used for this measurement include the reciprocal metre or inverse metre (symbol: m−1), and the reciprocal centimetre or inverse centimetre (symbol: cm−1).
In optics, the dioptre is a unit equivalent to reciprocal metre.
List of quantities
Quantities measured in reciprocal length include:
Measure of energy
In some branches of physics, a set of
natural units is adopted, such that 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 is proportional to the number of reciprocal length units. For example, in terms of energy, one reciprocal metre equals (one hundredth) as much as a reciprocal centimetre. Five reciprocal metres are five times as much energy as one reciprocal metre.
See also
Further reading
