Mica crystal viwed through the Fizeau interferometer
Birefringence is formally defined as the double refraction of light in a transparent, molecularly ordered material, which is manifested by the existence of orientation-dependent differences in refractive index. Many transparent solids are optically isotropic, meaning that the index of refraction is equal in all directions throughout the crystalline lattice. Examples of isotropic solids are glass, table salt (sodium chloride, illustrated in many polymers, and a wide variety of both organic and inorganic compounds.
The simplest crystalline lattice structure is cubic, as illustrated by the molecular model of sodium chloride in an arrangement where all of the sodium and chloride ions are ordered with uniform spacing along three mutually perpendicular axes. Each chloride ion is surrounded by (and electrostatically bonded to) six individual sodium ions and vice versa for the sodium ions. The lattice structure illustrated in represents the mineral calcite (calcium carbonate), which consists of a rather complex, but highly ordered three-dimensional array of calcium and carbonate ions. Calcite has an anisotropic crystalline lattice structure that interacts with light in a totally different manner than isotropic crystals. The polymer illustrated in is amorphous and devoid of any recognizable periodic crystalline structure. Polymers often possess some degree of crystalline order and may or may not be optically transparent.
Crystals are classified as being either isotropic or anisotropic depending upon their optical behavior and whether or not their crystallographic axes are equivalent. All isotropic crystals have equivalent axes that interact with light in a similar manner, regardless of the crystal orientation with respect to incident light waves. Light entering an isotropic crystal is refracted at a constant angle and passes through the crystal at a single velocity without being polarized by interaction with the electronic components of the crystalline lattice.