View source for Hagen–Rubens relation

{{Short description|Formula in optics}}
In [[optics]], the '''Hagen–Rubens relation''' (or '''Hagen–Rubens formula''') is a relation between the [[coefficient of reflection]] and the [[electrical conductivity|conductivity]] for materials that are good conductors.<ref>{{cite book|last=Ziman|first=J.M.|title=Principles of the theory of solids|date=1985|publisher=[[Cambridge University Press]]|location=Cambridge|isbn=0521297338|edition=2nd}}</ref> 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]]):<ref>{{cite book|last=Hummel|first=Rolf E.|title=Electronic properties of materials|publisher=Springer|location=New York|isbn=978-1441981646|edition=4th|date=2011-06-15}}</ref> 
<math>R\approx1-2\sqrt{\frac{2\epsilon_0\omega}{\sigma}} </math>

where <math>\omega</math> is the frequency of observation, <math>\sigma</math> is the conductivity, and <math>\epsilon_0</math> is the [[vacuum permittivity]]. For metals, this relation holds for frequencies (much) smaller than the [[Drude model|Drude relaxation rate]], and in this case the otherwise frequency-dependent conductivity <math>\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.<ref name=Hagen1903>{{cite journal|last1=Hagen|first1=E. |author2=Rubens, H. |title=Über Beziehungen des Reflexions‐ und Emissionsvermögens der Metalle zu ihrem elektrischen Leitvermögen |journal=Annalen der Physik |date=1903 |volume=316 |issue=8 |pages=873–901 |doi=10.1002/andp.19033160811 |url=https://zenodo.org/record/2301925 }}</ref><ref name=iop>{{cite journal|last=Silveira|first=F. E. M.|author2=Kurcbart, S. M.|title=Hagen-Rubens relation beyond far-infrared region|journal=EPL|date=1 May 2010|volume=90|issue=4|pages=44004|doi=10.1209/0295-5075/90/44004|bibcode = 2010EL.....9044004S }}</ref>

==References==
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{{DEFAULTSORT:Hagen-Rubens relation}}
[[Category:Scattering, absorption and radiative transfer (optics)]]
[[Category:Infrared spectroscopy]]
[[Category:Electric and magnetic fields in matter]]


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