Virbhadra–Ellis lens equation explained

The Virbhadra-Ellis lens equation ^[1] 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 - (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.

Notes and References

1. Virbhadra . K. S. . Ellis . George F. R. . Schwarzschild black hole lensing . Physical Review D . American Physical Society (APS) . 62 . 8 . 2000-09-08 . 0556-2821 . 10.1103/physrevd.62.084003 . 084003. astro-ph/9904193 . 2000PhRvD..62h4003V . 15956589 .