Light enters at an angle of incidence in a transparent rod of refractive index ' n '. The least value of ' n ' for which the light once entered into it will not leave it through its lateral face whatsoever be the value of the angle of incidence is

Step-by-step solution

Let the refractive index of the rod be n and the refractive index of the surrounding medium be 1 . Let the angle of incidence at the end face be i and the angle of refraction be r . By Snell's law at the end face, 1 (i) = n (r) . The light travels inside the rod and hits the lateral surface at an angle of incidence = 90^ - r . For the light not to leave the lateral surface, it must undergo total internal reflection. The condition for total internal reflection is ( ) 1 n . Substituting = 90^ - r , we get (r) 1 n . S