Refractive index

Remarks

In terms of the relative permittivity $\varepsilon_r$ and the relative permeability $\mu_r$ of the medium, $n = \sqrt{\varepsilon_r \mu_r}$. For an absorbing medium, $\varepsilon_r$ is complex, and one uses the complex index $\tilde{n} = n + i\kappa$, where $\kappa$ governs the decay of the wave. For a non-uniform medium, $n(x)$ is the index at each point $x$.

Example: in water, visible light has phase velocity about $2.25 \times 10^8$ m/s. Check: $n = (3.00 \times 10^8) / (2.25 \times 10^8) \approx 1.33$.

Non-example: in a birefringent crystal such as calcite, the phase velocity depends on the direction and polarization of the wave. The medium is not isotropic, and a single number $n$ does not describe it; one uses two or three principal indices instead.

The index is $1$ in vacuum and usually larger than $1$ in transparent matter, but $n < 1$ occurs, for example for X-rays in many materials.