question_answer 65)

  If light passes near a massive object, the gravitational interaction causes a bending of the ray. This can be thought of as happening due to a change in the effective refractive index of the medium given  by where r is the distance of the point of consideration from  the centre of the mass of the massive body, G is the universal gravitational constant, M the mass of the body and c the speed of light in vacuum. Considering a spherical object, find the deviation of the ray from the original path as it grazes the object

Answer:

                  In Fig. 6(EP).16, we have shown a spherical massive body of mass At and radius R. Consider two planes one at r and other at  from the centre of massive body. Let the light rays be incident at an angle 6 on the plane at r and leave the plane at  at an angle .                                 According to Snell?s law, As  is small,  and  sin . Neglecting products of differentials, we get Or              Or           AS               ?(i) Put in(i )  Integration both sides, we get Now, from Fig.6(EP).16,  and            If we put then      This is the deviation for the ray from the original path as it grazes the massive body.