One side of an equilateral prism is painted by a transparent material of refractive index n₂ . The refractive index of prism is 1.6 . The minimum value of n₂ required for total internal reflection from painted face is _______.

Step-by-step solution

Given that the prism is an equilateral triangle, all its refracting angles are 60^ . The incident ray falls normally on one of the faces of the prism. Therefore, the angle of incidence is 0^ and the ray enters the prism undeviated. From the geometry of the figure, the ray strikes the bottom painted face. In the right-angled triangle formed by the ray and the two faces of the prism, the angle between the left face and the bottom face is 60^ . The angle the refracted ray makes with the bottom face is 90^ - 60^ = 30^