Harman Patil (Editor)

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:

  • 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 6996124000000000000♠1.24×10−4 eV or 6977198600000000000♠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 6998100000000000000♠10−2 (one hundredth) as much as a reciprocal centimetre. Five reciprocal metres are one-fifth as much energy as one reciprocal metre.

    References

    Reciprocal length Wikipedia
    (Text) CC BY-SA