Hagen–Rubens relation - Misplaced Pages

(Redirected from Hagen-Rubens relation) Formula in optics

In optics, the Hagen–Rubens relation (or Hagen–Rubens formula) is a relation between the coefficient of reflection and the conductivity for materials that are good conductors. The relation states that for solids where the contribution of the dielectric constant to the index of refraction is negligible, the reflection coefficient can be written as (in SI Units):

R\approx 1-2{\sqrt {\frac {2\epsilon _{0}\omega }{\sigma }}}

where $\omega$ is the frequency of observation, $\sigma$ is the conductivity, and $\epsilon _{0}$ is the vacuum permittivity. For metals, this relation holds for frequencies (much) smaller than the Drude relaxation rate, and in this case the otherwise frequency-dependent conductivity $\sigma$ can be assumed frequency-independent and equal to the dc conductivity.

The relation is named after German physicists Ernst Bessel Hagen and Heinrich Rubens who discovered it in 1903.

References

Ziman, J.M. (1985). Principles of the theory of solids (2nd ed.). Cambridge: Cambridge University Press. ISBN 0521297338.
Hummel, Rolf E. (2011-06-15). Electronic properties of materials (4th ed.). New York: Springer. ISBN 978-1441981646.
Hagen, E.; Rubens, H. (1903). "Über Beziehungen des Reflexions- und Emissionsvermögens der Metalle zu ihrem elektrischen Leitvermögen". Annalen der Physik. 316 (8): 873–901. doi:10.1002/andp.19033160811.
Silveira, F. E. M.; Kurcbart, S. M. (1 May 2010). "Hagen-Rubens relation beyond far-infrared region". EPL. 90 (4): 44004. Bibcode:2010EL.....9044004S. doi:10.1209/0295-5075/90/44004.

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