# Refractive index

From AMS Glossary

## refractive index

(

*Or*index of refraction; also absolute refractive index.) The ratio of the free- space speed of light*c*, a universal constant, to the phase velocity of a plane harmonic electromagnetic wave in an optically homogeneous, unbounded medium.The refractive index, often denoted as where θ where where ω is circular frequency. Here the real part where λ is the free-space wavelength. The inverse of the absorption coefficient is the distance over which the irradiance of a plane wave is attenuated (by absorption) by the factor in which instance the absorption coefficient is where λ is the wavelength in the medium. Two widespread myths about

*n*, of a given material in a given state depends on the frequency of the plane wave. A plane harmonic wave incident on an optically smooth interface between two dissimilar, negligibly absorbing media undergoes a change in direction specified by Snel's law (attributed to Willebrord Snel, almost always misspelled as Snell):_{i}is the angle between the normal to the interface and the wave vector of the (incident) wave in the medium with refractive index*n*_{i}, and θ_{t}is the angle between the normal to the interface and the wave vector of the (transmitted or refracted) wave in the medium with refractive index*n*_{t}. The ratio*n*_{t}/*n*_{i}is the relative refractive index. Strictly speaking, plane harmonic wave propagation in an unbounded, homogeneous medium is specified by a complex refractive index, sometimes written as*n*and*k*are nonnegative but otherwise unrestricted. The choice of sign depends on the convention for harmonic time dependence,*n*is as defined previously, and the imaginary part*k*, sometimes called the absorption index, is related to the absorption coefficient by*e*. Although the real part of the complex refractive index is often denoted as*n*, no symbol is widely used for the imaginary part. In particular, the complex refractive index is sometimes written*n*are that it can never be less than 1 and that it stands in a one-to-one relation with (mass) density. For a refutation of the first see Brillouin (1960); for a refutation of the second see Barr (1955).Brillouin, L. 1960. Wave Propagation and Group Velocity.

Barr, E. S. 1955. Amer. J. Phys.. 623–624.