Question

A ray of light traveling in air is incident at angle theta_a on one face of a 90 degree prism made of glass. Part of the light refracts into the prism and strikes the opposite face at point A. If the ray at A is at the critical angle, what is the value of theta_a. See diagram to right.

Answer 1

Let n_glass = reflection index of glass = 1.40 n_air = refractive index of air = 1 critical angle theta_c = sin^-1(1/1.40) = 45.58 degree angle AED = 90 -theta_c = 90 -45.38 = 44.41 angle ADE = 180 -90 -44.41 = 45.38 angle B = 90 -45.38 = 44.41 degree from snells law: n_air times sin theta_a = n_glass times air beta sin theta_a = 1.40 times sin(44.41) = 0.98 theta_a = 78.46 hence angle of incidence theta_a = 78.46 degree