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).

[1] What are the average speeds for the ordinary and extraordinary ray in calcite?

[2] What are the wavelengths for each ray inside the crystal?

[3] For light with wavelength 600nm, what thickness of calcite will give a phase shift of ? between the ordinary and extraordinary rays?

[4] What is the optical path difference (in number of wavelengths) between the waves for a thickness of 0.445mm?

[5] A ray is incident on a piece of calcite at an angle of 30A????1 from the normal to the surface. The optic axis is parallel to the surface of the crystal and the incoming ray is unpolarized. Calculate the angle between the two polarized rays in the crystal using Snell's law and the two indices of refraction.

[6] If the crystal is 1cm thick, calculate the distance between the points where the two polarized rays emerge from the crystal.