A right-isosceles prism (angles 45∘, 45∘, 90∘) made of flint glass with index of refraction n=1.52 is used in a periscope. A light ray in air strikes one of the prism’s legs perpendicularly (along the normal) and then travels inside the prism until it reaches the hypotenuse.
(a) On a labeled sketch of the prism, draw the incident, refracted, and reflected portions of the light path, indicating all relevant angles with respect to the normals at each interface.
(b) Determine the angle of incidence of the ray on the hypotenuse from within the glass.
(c) Decide whether the ray undergoes total internal reflection at the hypotenuse. Support your answer with numerical justification.
(d) If total internal reflection does not occur for part (c), compute the minimum index of refraction the prism material would need so that total internal reflection does occur under the same geometry.