# Gravitational Lensing deflection angle question

1. Jul 28, 2011

### GuitaristOfRa

I wasn't sure whether this was the right place to post this since it isn't really coursework, but it seems like it could be.

My problem is with the deflection angle of light for several point masses.

The deflection for a point mass can be described as:

$\frac{4GM}{c^{2}\xi}$

where $\xi$ is the minimum distance between the light and the lens.

For a thin lens approximation of several point masses, the equation for the deflection angle is:

$\sum$$\frac{4Gm_{i}}{c^{2}}$$\frac{\xi-\xi_{i}}{|\xi-\xi_{i}|^{2}}$

where $\xi$ is the position of the light ray in the lens plane and $\xi_{i}$ is the position of the mass $m_{i}$. (they are vectors)

It seems to me to be a direct extension of the point mass equation, but I don't understand where the $\frac{\xi-\xi_{i}}{|\xi-\xi_{i}|^{2}}$ comes from. It seems to me that it would just be $\frac{1}{\xi-\xi_{i}}$. Can anyone explain it?