Special & General Relativity Questions and Answers
Can you use the geometry of gravitational lenses to determine the distances to the lensed quasar?
So far as I know, the answer is yes. Have a look at a paper published in the Astrophysical Journal in 1995 that 'solves' for the geometry in the particular case of a lens source detected by the Hubble Space Telescope.
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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.