# Reciprocal length

Reciprocal length or inverse length is a 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: m1), the reciprocal centimetre or inverse centimetre (symbol: cm1), and, in optics, the dioptre.

Quantities measured in reciprocal length include:

## Measure of energy

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. Therefore, as reciprocal length is a measure of frequency, it can also be used as a measure of energy. For example, the reciprocal centimetre, cm−1, is an energy unit equaling the energy of a photon with 1 cm wavelength. That energy amounts to approximately 1.24×10−4 eV or 1.986×10−23 J.

The higher the number of inverse length units, the higher the energy. For example, in terms of energy, one reciprocal metre equals 10−2 (one hundredth) as much as a reciprocal centimetre.

• Barrett, A. J. (11 July 1983). "A two-parameter perturbation series for the reciprocal length of polymer chains and subchains". Journal of Physics A: Mathematical and General. 16 (10): 2321–2330. Bibcode:1983JPhA...16.2321B. doi:10.1088/0305-4470/16/10/027.