When Einstein meets Huygens

Classical Mechanics Level 5

In Einstein's theory of gravity an electromagnetic wave passing near a massive object is bent from its rectilinear path. We may regard this bending equivalently as due to a medium of refractive index $n$ given by $n=1-\frac {2V}{c^2}$ , where $V$ denotes the gravitational potential due to object of mass $M$ . If the angle of deflection $\theta$ of the light coming from the distant object is $\theta=\frac {kGM}{bc^2}$ , where $b$ is the impact parameter (closest distance of approach), compute $k^2$ .

The answer is 16.

1 solution

Richeek Das
Jan 14, 2019

Well , I did this problem by finding the deviation angle using :

$\alpha$ = $\frac{2}{c^{2}}$ $\int_{-\infty}^{+\infty} \nabla \phi dz$

Where $\phi$ denotes Gravitational Potential ,i.e ; $\phi$ = $\frac{GM}{r}$ , where $r$ = $\sqrt{b^{2}+z^{2}}$

I will be glad , if someone points out some other elegant way of doing this sum !

When Einstein meets Huygens

The answer is 16.

1 solution

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