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

where $\omega$ is the frequency of observation, $\sigma$ is the conductivity, and $\epsilon _{0}$ is the vacuum permittivity.

The relation is named after German physicists Ernst Bessel Hagen and Heinrich Rubens in 1903, who discovered it in 1903.^[3]

References

1. Ziman, J.M. (1985). Principles of the theory of solids (2nd ed.). Cambridge: Cambridge University Press. ISBN 0521297338.
2. Hummel, Rolf E. Electronic properties of materials (4th ed.). New York: Springer. ISBN 1441981640.
3. Silveira, F. E. M.; Kurcbart, S. M. (1 May 2010). "Hagen-Rubens relation beyond far-infrared region". EPL (Europhysics Letters). 90 (4): 44004. Bibcode:2010EL.....9044004S. doi:10.1209/0295-5075/90/44004. Retrieved 15 April 2013.