# Help! Deriving formula for Einstein Radius

1. Feb 19, 2008

I have been trying to show that the Einstein ring radius R_e = 2[GMx(L-x)/(Lc^2)]^1/2
to no avail. can someone who knows this show me, or at least point out the direction. I have a strong hunch that i'll have to use the light bending formula for small angles 
delta_phi = 4GM/(bc^2), and geometry.

The Einstein radius is the radius of the ring image formed when a bright source is exactly behind a spherically symmetric lens mass. L is the distance to the source, and x is the distance to the lens mass.

2. Feb 19, 2008

### George Jones

Staff Emeritus
The formula on http://en.wikipedia.org/wiki/Einstein_ring" [Broken] can be derived using the light bending formula for small angles. Also, assume Euclidean geometry and use $\theta \doteq \sin\theta \doteq \tan\theta$. Click on the diagram, and take $\theta_S = 0$, since, for an Einstein ring, the source, lens, and observer have to be lined up.

If you need more help, just ask.

Last edited by a moderator: May 3, 2017