Virbhadra–Ellis lens equation

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

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

This approximate lens equation is useful for studying the gravitational lens in strong and weak gravitational fields when the angular source position is small.