Question

The equilateral glass prism shown has an index of refraction of 1.54. The prism is surrounded by air. A ray of light is incident on the middle of the left face of theprism. What is the smallest angle of incidence for which the ray of light will emerge from the right face of the prism?

Answer 1

Giventhe prism is a equilateral glass prism which has an apex angle 60^ o and refractive index n = 1.54For the light to emerge, the angle of incidence c inside the prism at the second face must satisfy
sin(c) <= 1 / 1.54
c <=40.4926deg.
The angle of refraction from the first face is r where:
r >=60 -40.492
r >= 19.5^ o.
Apply snells law
sin ? >= 1.54 sin(r)
sin ? >= 1.54( sin 19.5)= 0.5142? =30.94 degrees