A light ray passes through an equilateral glass prism such that the angle of incidence is equal to the angle of emergence. If each of these angles is equal to 3 4 of the angle of the prism, the refractive index of the material of the prism is x . The value of x is ________.

Step-by-step solution

For an equilateral prism, the angle of the prism A = 60^ . Given that the angle of incidence i and the angle of emergence e are equal, the prism is in the position of minimum deviation. The angle of incidence is given by i = 3 4 A = 3 4 60^ = 45^ . At minimum deviation, the angle of refraction at the first face is r = A 2 = 60^ 2 = 30^ . Using Snell's law, the refractive index is: = i r = 45^ 30^ = 1/ 2 1/2 = 2 Given that = x , we have x = 2 , which gives x = 2 . Answer: 2