2. A special prism
A particularly useful optical element
(readily available from optics supply companies) is made of a piece of
calcite in the form of a rectangular prism. Light enters one face at normal
incidence and travels the length of the prism, emerging from the opposite
face (which is of course parallel to the entrance face). The prism is 62
mm long (in the beam-path direction), and the optic axis of the calcite
is at an angle of 42° to the normal to the entrance and exit faces. What is the effect
of this prism on unpolarized light? Be quantitative. Why is the optic axis
of the calcite made to be at this particular angle to the entrance and
exit faces?
Solution to problem 2
3. Ammann-Massey prism
Another special prism is made two wedges. The right-hand wedge is made of calcite (mo = 1.6584, me = 1.4864) with the optic axis oriented vertically in the plane of the page. The left-hand wedge is made of glass, carefully chosen so that its index mg is equal to the ordinary index of calcite. The wedge angle is 70°, and the two wedges are glued together with an optical cement that also has index mg. Describe what happens when unpolarized light is incident normally on the left face of the prism. Then describe what happens when light is incident from the other side, i.e. on the right face of the prism.
4. Selecting the wavelength
A parallel (collimated) beam of light from a sodium lamp passes through a pair of polarizers whose axes are oriented in the same direction. Between the two polarizers is a calcite plate whose optic axis is in the plane of its faces, oriented at 45° to the axes of the polarizers. One of the two lines of the yellow doublet (the closely-spaced pair of spectral lines near 589 nm) is transmitted through this "sandwich" and the other is absorbed. How thick is the calcite plate?
Useful information: In this wavelength range, the refractive indices of calcite and their dispersion (dependence on wavelength) are:
mo
= 1.486, me
= 1.658, 
= - 3.53 x 10-5
nm-1, 
= - 5.88 x 10-5 nm-1
Solution to problem 4