A birefringent material has two different refractive indices because of the crystal symmetry. Such crystals have an optical axis associated with one index and two equivalent axes (perpendicular to the optic axis in calcite) associated with the other index. A ray with its polarization (E field) along the optical axis (called the ordinary ray) experiences one refractive index (1.65 for calcite) while a ray with its polarization perpendicular to the optic axis ( an extraordinary ray) experiences a different refractive axis (1.486 for calcite).
A ray is incident on a piece of calcite at an angle of 30o from the normal to the surface. The optic axis is parallel to the surface of the crystal and the incoming ray is unpolarized.
[A] Calculate the angle between the two polarized rays in the crystal using Snell's law and the two indices of refraction.
[B] If the crystal is 1cm thick, calculate the distance between the points where the two polarized rays emerge from the crystal.