Editing Refractive index (section)

===Birefringence===
{{Main|Birefringence}}

[[File:Calcite.jpg|thumb|alt=A crystal giving a double image of the text behind it|A [[calcite]] crystal laid upon a paper with some letters showing [[double refraction]]]]
[[File:Plastic Protractor Polarized 05375.jpg|thumb|alt=A transparent plastic protractor with smoothly varying bright colors| Birefringent materials can give rise to colors when placed between crossed polarizers. This is the basis for [[photoelasticity]].]]

In some materials, the refractive index depends on the [[Polarization (waves)|polarization]] and propagation direction of the light.<ref>R. Paschotta, article on [https://www.rp-photonics.com/birefringence.html birefringence] {{webarchive|url=https://web.archive.org/web/20150703221334/http://www.rp-photonics.com/birefringence.html |date=2015-07-03 }} in the [https://www.rp-photonics.com/encyclopedia.html Encyclopedia of Laser Physics and Technology] {{webarchive|url=https://web.archive.org/web/20150813044135/http://www.rp-photonics.com/encyclopedia.html |date=2015-08-13 }}, accessed on 2014-09-09</ref> This is called [[birefringence]] or optical [[anisotropy]].

In the simplest form, uniaxial birefringence, there is only one special direction in the material. This axis is known as the [[Optic axis of a crystal|optical axis]] of the material.<ref name=Hecht/>{{rp|230}} Light with linear polarization perpendicular to this axis will experience an ''ordinary'' refractive index {{math|''n''{{sub|o}}}} while light polarized in parallel will experience an ''extraordinary'' refractive index {{math|''n''{{sub|e}}}}.<ref name=Hecht/>{{rp|236}} The birefringence of the material is the difference between these indices of refraction, {{math|Δ''n'' {{=}} ''n''{{sub|e}} − ''n''{{sub|o}}}}.<ref name=Hecht/>{{rp|237}} Light propagating in the direction of the optical axis will not be affected by the birefringence since the refractive index will be {{math|''n''{{sub|o}}}} independent of polarization. For other propagation directions the light will split into two linearly polarized beams. For light traveling perpendicularly to the optical axis the beams will have the same direction.<ref name=Hecht/>{{rp|233}} This can be used to change the polarization direction of linearly polarized light or to convert between linear, circular, and elliptical polarizations with [[waveplate]]s.<ref name=Hecht/>{{rp|237}}

Many [[crystal]]s are naturally birefringent, but [[isotropic]] materials such as [[plastic]]s and [[glass]] can also often be made birefringent by introducing a preferred direction through, e.g., an external force or electric field. This effect is called [[photoelasticity]], and can be used to reveal stresses in structures. The birefringent material is placed between crossed [[polarizers]]. A change in birefringence alters the polarization and thereby the fraction of light that is transmitted through the second polarizer.

In the more general case of trirefringent materials described by the field of [[crystal optics]], the ''dielectric constant'' is a rank-2 [[tensor]] (a 3 by 3 matrix). In this case the propagation of light cannot simply be described by refractive indices except for polarizations along principal axes.