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(Dds\right)

and observer-source

\left(Ds\right)

distances.

\tan\beta=\tan\theta-

Dds
Ds

\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 .