A ray of monochromatic light passes through an equilateral prism such that the refracted ray inside the prism is parallel to its base. If the angle of deviation of the ray is 60^ , what is the critical angle of the prism material with respect to air?

Step-by-step solution

For an equilateral prism, the angle of the prism is A = 60^ . The refracted ray is parallel to the base, meaning the prism is in the position of minimum deviation. In this state, the angle of refraction is r = A 2 = 30^ . The angle of deviation is given as = 60^ . Using the formula for minimum deviation: = 2i - A 60^ = 2i - 60^ 2i = 120^ i = 60^ The refractive index of the prism material is: = i r = 60^ 30^ = 3 2 1 2 = 3 The critical angle _c of the prism material with respect to air is given by: _c = 1 _c = 1 3 _c