Hagen–Rubens relation

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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\approx1-2\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]


  1. ^ Ziman, J.M. (1985). Principles of the theory of solids (2nd ed. ed.). Cambridge: Cambridge University Press. ISBN 0521297338. 
  2. ^ Hummel, Rolf E. Electronic properties of materials (4th ed. 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.