Virbhadra–Ellis lens equation

The Virbhadra–Ellis lens equation ^[1] relates angular positions of an unlensed source ${\displaystyle \left(\beta \right)}$, the image ${\displaystyle \left(\theta \right)}$, the Einstein bending angle of light ${\displaystyle ({\hat {\alpha }})}$, and the angular diameter lens-source ${\displaystyle \left(D_{ds}\right)}$ and observer-source ${\displaystyle \left(D_{s}\right)}$ distances.

${\displaystyle \tan \beta =\tan \theta -{\frac {D_{ds}}{D_{s}}}\left[\tan \theta +\tan \left({\hat {\alpha }}-\theta \right)\right]}$.

This lens equation is useful for studying gravitational lensing in a strong gravitational field. 

This article uses material from the Wikipedia article  Metasyntactic variable, which is released under the  Creative Commons Attribution-ShareAlike 3.0 Unported License.