Bending of Light rays!

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 \(\large n(r) = 1 + 2\frac{GM}{rc^2}\) 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 \(\theta_0\) from the original path as it grazes the object.

If \(\large \theta_0 = n_1\frac{GM}{rc^{n_2}}\), find \(n_1 + n_2\).

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