A ray of monochromatic light is incident on the vertical left face of a transparent rectangular block at an angle of incidence of 60^ , as shown in the figure. After refracting into the block, the ray strikes its top horizontal face. If the ray emerges such that it just grazes the top surface of the block, what is the refractive index of the material of the block?

Step-by-step solution

Let the refractive index of the material of the block be n . At the first refracting surface (vertical left face), the angle of incidence is i = 60^ . Let the angle of refraction be r . Applying Snell's law: 1 60^ = n r n r = 3 2 ... (1) Inside the block, the ray strikes the top horizontal face. Since the normal to the vertical face is horizontal and the normal to the top face is vertical, the angle of incidence at the top face is 90^ - r . The problem states that the ray emerges grazing the top surface, which mean