Light is incident in air at an angle ua (Fig. P33.54) on the upper surface of a transparent plate, the surfaces of the plate being plane and parallel to each other.

(a) Prove that θ_a = θ'a.

(b) Show that this is true for any number of different parallel plates.

(c) Prove that the lateral displacement d of the emergent beam is given by the relationship

where t is the thickness of the plate.

(d) A ray of light is incident at an angle of 66.0° on one surface of a glass plate 2.40 cm thick with an index of refraction of 1.80. The medium on either side of the plate is air. Find the lateral displacement between the incident and emergent rays.

Figure P33.54

sin(0. 0'b) d = t cos 8' Pi