Reciprocal length

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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 (m−1), the reciprocal centimetre or inverse centimetre (cm−1), and, in optics, the dioptre.

Quantities measured in reciprocal length include:

Measure of energy[edit]

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 lower the energy. For example, in terms of energy, one reciprocal metre equals 10−2 (one hundredth) as much as a reciprocal centimetre. Five reciprocal metres are one-fifth as much energy as one reciprocal metre.

Further reading[edit]