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 center 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.

Given:

The change in the effective refractive index of the medium given by, r is the distance from the center of mass, G is the universal gravitational constant, M the mass of the body and c the speed of light in vacuum, To find the angle of deviation we need to find the relation between angle of incidence and refractive index in terms of mass, gravity and speed of light.

Formula Used:

Applying Snell’s Law, Snell’s Law, is the ratio between the sine value of incidence and refraction with the ratio of refractive index of the mediums through which the light passes and the second formula applied is the Gravitational Radiation Shift, the shift occurs when passing through a gravitational field with loss of energy changing the refractive index of the light.

where

is the refractive index of the medium, is the refractive index of the air. i is the angle of incidence and r is the angle of refraction.

where

G is the universal gravitational constant, M is the mass of the earth, r is the distance from the center of the mass and c is the speed of light = .

Explanation:

Using Snell’s Law,

Putting in place of and and

After integration we get

Therefore, the angle of deviation is. Answer