A ray of light undergoes minimum deviation as it passes through a prism of angle 60^ and refractive index 3 . After emerging from the prism, the ray strikes a plane mirror. The mirror is oriented such that the reflected ray becomes anti-parallel to the original incident ray. The angle of incidence of the ray on the plane mirror (in degrees) is _______.

Step-by-step solution

For the prism, the angle A = 60^ and refractive index = 3 . At minimum deviation, the angle of refraction inside the prism is r = A 2 = 30^ . Using Snell's law at the first surface: 1 (i) = (r) (i) = 3 (30^ ) = 3 2 i = 60^ The deviation produced by the prism is: _p = 2i - A = 2(60^ ) - 60^ = 60^ For the final reflected ray to be anti-parallel to the original incident ray, the total deviation of the ray must be 180^ . Let the deviation produced by the plane mirror be _m . Since the deviations are in the same sense: