optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...

, 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. 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 The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official st ...

): :

R\approx1-2\sqrt

where

\omega

is the frequency of observation,

\sigma

is the conductivity, and

\epsilon_0

is the

vacuum permittivity Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric const ...

. 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 Heinrich Rubens (; 30 March 1865 – 17 July 1922) was a German physicist. He is known for his measurements of the energy of black-body radiation which led Max Planck to the discovery of his Planck's law, radiation law. This was the genesis of Qu ...

who discovered it in 1903.

References

Scattering, absorption and radiative transfer (optics) Infrared spectroscopy Electric and magnetic fields in matter {{spectroscopy-stub