Reciprocal length
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, and the reciprocal centimetre or inverse centimetre.
In optics, the dioptre is a unit equivalent to reciprocal metre.
List of 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
- surface area to volume ratio
Measure of energy
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 as much as a reciprocal centimetre. Five reciprocal metres are five times as much energy as one reciprocal metre.