# Lorentz-Lorenz relation  Main Article Discussion Related Articles  [?] Bibliography  [?] External Links  [?] Citable Version  [?] This editable Main Article is under development and subject to a disclaimer. [edit intro]

In physics, the Lorentz-Lorenz relation is an equation between the index of refraction n and the density ρ of a dielectric (non-conducting matter),

${\frac {n^{2}-1}{n^{2}+2}}=K\,\rho ,$ where the proportionality constant K depends on the polarizability of the molecules constituting the dielectric.

The relation is named after the Dutch physicist Hendrik Antoon Lorentz and the Danish physicist Ludvig Valentin Lorenz.

For a molecular dielectric consisting of a single kind of non-polar molecules, the proportionality factor K (m3/kg) is,

$K={\frac {P_{M}}{M}}\times 10^{3},$ where M (g/mol) is the the molar mass (formerly known as molecular weight) and PM (m3/mol) is (in SI units):

$P_{M}={\frac {1}{3\epsilon _{0}}}N_{\mathrm {A} }\alpha .$ Here NA is Avogadro's constant, α is the molecular polarizability of one molecule, and ε0 is the electric constant (permittivity of the vacuum). In this expression for PM it is assumed that the molecular polarizabilities are additive; if this is not the case, the expression can still be used when α is replaced by an effective polarizability. The factor 1/3 arises from the assumption that a single molecule inside the dielectric feels a spherical field from the surrounding medium. Note that α / ε0 has dimension volume, so that K indeed has dimension volume per mass.

In Gaussian units (a non-rationalized centimeter-gram-second system):

$P_{M}={\frac {4\pi }{3}}N_{\mathrm {A} }\alpha ,$ and the factor 103 is absent from K (as is ε0, which is not defined in Gaussian units).

For polar molecules a temperature dependent contribution due to the alignment of dipoles must be added to K.

The Lorentz-Lorenz law follows from the Clausius-Mossotti relation by using that the index of refraction n is approximately (for non-conducting materials and long wavelengths) equal to the square root of the static relative permittivity (formerly known as static relative dielectric constant) εr,

$n\approx {\sqrt {\varepsilon _{r}}}.$ In this relation it is presupposed that the relative permeability μr equals unity, which is a reasonable assumption for diamagnetic and paramagnetic matter, but not for ferromagnetic materials.