Editing Crystal optics (section)

==Isotropic media==

Typical transparent media such as [[glass]]es are ''[[isotropic]]'', which means that light behaves the same way no matter which direction it is travelling in the medium. In terms of [[Maxwell's equations]] in a [[dielectric]], this gives a relationship between the [[electric displacement field]] '''D''' and the [[electric field]] '''E''':

:<math> \mathbf{D} = \varepsilon_0  \mathbf{E} + \mathbf{P}  </math>

where ε<sub>0</sub> is the [[permittivity]] of free space and '''P''' is the electric [[polarization (electrostatics)|polarization]] (the [[vector field]] corresponding to [[electric dipole moment]]s present in the medium). Physically, the polarization field can be regarded as the response of the medium to the electric field of the light.

===Electric susceptibility===

In an [[isotropic]] and [[linear]] medium, this polarization field '''P''' is proportional and parallel to the electric field '''E''':

:<math> \mathbf{P}  = \chi \varepsilon_0 \mathbf{E}  </math>

where χ is the ''[[electric susceptibility]]'' of the medium. The relation between '''D''' and '''E''' is thus:

:<math> \mathbf{D}  =   \varepsilon_0 \mathbf{E}  +  \chi \varepsilon_0 \mathbf{E}   
=  \varepsilon_0  (1 + \chi)  \mathbf{E}   =  \varepsilon   \mathbf{E}  </math>

where

:<math> \varepsilon =  \varepsilon_0  (1 + \chi) </math>

is the [[dielectric constant]] of the medium.  The value 1+χ is called the ''relative permittivity'' of the medium, and is related to the [[refractive index]] ''n'', for non-magnetic media, by

:<math>  n = \sqrt{ 1 + \chi}  </math>