Virbhadra–Ellis lens equation

The Virbhadra–Ellis lens equation ^[1] relates angular positions of the 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 lens equation is mainly useful for studying gravitational lensing in a strong gravitational field (see here for more information.)

References

↑ K.S. Virbhadra and G. F.R. Ellis, Phys. Rev. D62, 084003 (2000).

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