Discuss the results of Problem 4.38 in the light of Fermat€™s Principle; that is, how does the relative index n₂₁affect things? To see the lateral displacement, look at a broad source through a thick piece of glass ( ‰ˆ 1/4 inch) or a stack (four will do) of microscope slides held at an angle. There will be an obvious shift between the region of the source seen directly and the region viewed through the glass.

Data from Prob. 4.38

Show analytically that a beam (in a medium of index n₁) entering a planar transparent plate (of index n₂ and thickness d ), as in Fig. P.4.38, emerges parallel to its initial direction. Derive an expression for the lateral displacement (α) of the beam. Incidentally, the incoming and outgoing rays would be parallel even for a stack of plates of different material.

Fig. P.4.38