Question

A ray of light, incident on the face AB of a prism (made from a material of refractive index μ ) gets refracted there and falls on its other face AC. If it were to go grazing along this face, the angle of refraction (< r), at the face AB, would equal

(1) (A + sin^-1 1/μ) as well as sin^-1 [sin {cos^-1(sin (A+D))}]

(2) (A + sin^-1 1/μ) as well as sin^-1 [cos {sin^-1(cos (A+D))}]

(3) (A - sin^-1 1/μ) as well as sin^-1 [cos {sin^-1(cos (A+D))}]

(4) (A - sin^-1 1/μ) as well as sin^-1 [sin {cos^-1(sin (A+D))}]

Answer 1

(4) (A - sin^-1 1/μ) as well as sin^-1 [sin {cos^-1(sin (A+D))}]

It is clear that the angle of emergence, at the face AC, is 90° . The angle of incidence (say r’), at the face

AC, must equal the critical angle (= sin^-1 1/μ) for the material of the given prism.

We have r + r’ = A