Crystalline materials can have different indices of refraction in different crystallographic directions. Crystals belonging to the hexagonal, tetragonal, or rhombohedral classes are uniaxial
, in that they possess a unique optical axis,
most often coincident with the crystallographic
axis. Light traveling through such an anisotropic medium can exhibit double refraction
, in which an unpolarized incident light ray splits into two polarized rays with mutually perpendicular planes of vibration. The ray with its electric field vibrating perpendicular to the optical axis is called the ordinary
ray, and is characterized by an index of refraction
. The ray that vibrates parallel to the optical axis is called the extraordinary
ray, with its index of refraction designated
. The birefringence
is the difference Δ
, which can be positive or negative.
The best-known birefringent crystal is the mineral calcite (Iceland spar), the colorless, transparent rhombohedral salt calcium carbonate,
. The optical axis coincides with the three-fold axes of the equilateral
groups, along which the
ions are also situated. For 590 nm light, the yellow sodium-D lines, the indices for calcite are
0.172. Some other common uniaxial minerals are: tourmaline, beryl, quartz, ruby, sapphire and zircon. Birefringent materials find several applications in optics, for example Nicol prisms and quarter-wave plates.
In this Demonstration, the angle of incidence of a light ray entering a crystal can be varied, as can the two refractive indices (the default values are those of calcite). The direction of the optical axis is marked with a gray arrow. The ordinary ray is shown in orange, the extraordinary ray in blue. After refraction by the crystal, the light emerges in two parallel rays. You also have the option to display the polarizations of the various rays.