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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 refrative index of the medium given by 

n(r) = 1 + 2 GM/rc2 

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.

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Consider two planes at r and r + dr. Let the light be incident at an angle θ at the plane at r and leave r + dr at an angle θ +dθ

Then from Snell’s law

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