Editing Birefringence (section)

===Double refraction===
When an arbitrary beam of light strikes the surface of a birefringent material at non-normal incidence, the polarization component normal to the optic axis (ordinary ray) and the other linear polarization (extraordinary ray) will be refracted toward somewhat different paths. Natural light, so-called [[Polarization (waves)#Unpolarized and partially polarized light|unpolarized light]], consists of equal amounts of energy in any two orthogonal polarizations. Even linearly polarized light has some energy in both polarizations, unless aligned along one of the two axes of birefringence. According to [[Snell's law]] of refraction, the two angles of refraction are governed by the effective [[refractive index]] of each of these two polarizations. This is clearly seen, for instance, in the [[Wollaston prism]] which separates incoming light into two linear polarizations using prisms composed of a birefringent material such as [[calcite]].

The different angles of refraction for the two polarization components are shown in the figure at the top of this page, with the optic axis along the surface (and perpendicular to the [[plane of incidence]]), so that the angle of refraction is different for the {{mvar|p}} polarization (the "ordinary ray" in this case, having its electric vector perpendicular to the optic axis) and the {{mvar|s}} polarization (the "extraordinary ray" in this case, whose electric field polarization includes a component in the direction of the optic axis). In addition, a distinct form of double refraction occurs, even with normal incidence, in cases where the optic axis is not along the refracting surface (nor exactly normal to it); in this case, the [[dielectric polarization]] of the birefringent material is not exactly in the direction of the wave's [[electric field]] for the extraordinary ray. The direction of power flow (given by the [[Poynting vector]]) for this [[inhomogenous wave]] is at a finite angle from the direction of the [[wave vector]] resulting in an additional separation between these beams. So even in the case of normal incidence, where one would compute the angle of refraction as zero (according to Snell's law, regardless of the effective index of refraction), the energy of the extraordinary ray is propagated at an angle. If exiting the crystal through a face parallel to the incoming face, the direction of both rays will be restored, but leaving a ''shift'' between the two beams. This is commonly observed using a piece of calcite cut along its natural cleavage, placed above a paper with writing, as in the above photographs. On the contrary, [[waveplate]]s specifically have their optic axis ''along'' the surface of the plate, so that with (approximately) normal incidence there will be no shift in the image from light of either polarization, simply a relative [[phase shift]] between the two light waves.