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Help! Deriving formula for Einstein Radius

  1. Feb 19, 2008 #1
    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. jcsd
  3. Feb 19, 2008 #2

    George Jones

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    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 [itex]\theta \doteq \sin\theta \doteq \tan\theta[/itex]. Click on the diagram, and take [itex]\theta_S = 0[/itex], 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
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