Physics:Hagen–Rubens relation
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.[1] 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):[2] [math]\displaystyle{ R\approx1-2\sqrt{\frac{2\epsilon_0\omega}{\sigma}} }[/math]
where [math]\displaystyle{ \omega }[/math] is the frequency of observation, [math]\displaystyle{ \sigma }[/math] is the conductivity, and [math]\displaystyle{ \epsilon_0 }[/math] 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 [math]\displaystyle{ \sigma }[/math] 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.[3][4]
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. https://zenodo.org/record/2301925.
- ↑ Silveira, F. E. M.; Kurcbart, S. M. (1 May 2010). "Hagen-Rubens relation beyond far-infrared region". EPL 90 (4): 44004. doi:10.1209/0295-5075/90/44004. Bibcode: 2010EL.....9044004S.
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