The Lorentz–Lorenz equation, also known as the Clausius–Mossotti relation and Maxwell's formula, relates the refractive index of a substance to its polarizability. Named after Hendrik Antoon Lorentz and Ludvig Lorenz.
The most general form of the Lorentz–Lorenz equation is
where
When the polarizibility is small (such that |n-1| << 1) the equation reduces to:
or simply
This applies to gasses at ordinary pressures. The refractive index
where
History
The Lorentz–Lorenz equation is named after the Danish mathematician and scientist Ludvig Lorenz, who published it in 1869, and the Dutch physicist Hendrik Lorentz, who discovered it independently in 1878.