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 `n( r) = 1+ 2 GM//rc^2`
where `r` is the distance of the point 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.

Explanation

To find the deviation of a ray of light as it grazes a massive spherical object, we will follow these steps:

### Step 1: Understanding the Effective Refractive Index
The effective refractive index \( n(r) \) of the medium around a massive object is given by:
\[ n(r) = 1 + \frac{2GM}{rc^2} \]
where \( G \) is the universal gravitational constant, \( M \) is the mass of the object, \( r \) is the distance from the center of the mass, and \( c \) is the speed of light in vacuum.
...