Hagen–Rubens relation explained

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]

R ≈ 1-2\sqrt{2\epsilon0\omega
\sigma
}

where

\omega

is the frequency of observation,

\sigma

is the conductivity, and

\epsilon0

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.[3] [4]

Notes and References

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