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: m−1), the reciprocal centimetre or inverse centimetre (symbol: cm−1), and, in optics, the dioptre.
Quantities measured in reciprocal length include:
- absorption coefficient or attenuation coefficient, in materials science
- curvature of a line, in mathematics
- gain, in laser physics
- magnitude of vectors in reciprocal space, in crystallography
- more generally any spatial frequency e.g. in cycles per unit length
- optical power of a lens, in optics
- rotational constant of a rigid rotor, in quantum mechanics
- wavenumber, or magnitude of a wavevector, in spectroscopy
- density of a linear feature in hydrology and other fields; see kilometre per square kilometre
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.