A right-angled prism has acute angles of 30^ and 60^ . A ray of monochromatic light is incident normally on the face adjacent to the 90^ and 30^ angles. The ray strikes the hypotenuse and emerges into the surrounding air. If the angle of emergence from the hypotenuse is 45^ , what is the refractive index of the material of the prism?

Step-by-step solution

The ray is incident normally on the face adjacent to the 90^ and 30^ angles. Therefore, it enters the prism undeviated and travels parallel to the base (the face adjacent to the 90^ and 60^ angles). When the ray strikes the hypotenuse, the angle between the hypotenuse and the base is 60^ . Since the ray is parallel to the base, the angle between the incident ray and the hypotenuse is also 60^ . The angle of incidence i is measured from the normal to the surface. Thus, i = 90^ - 60^ = 30^ . Applying Snell's law at t