Virbhadra–Ellis lens equation

{{Technical|date=January 2022}}

The Virbhadra-Ellis lens equation {{cite journal | last1=Virbhadra | first1=K. S. | last2=Ellis | first2=George F. R. | title=Schwarzschild black hole lensing | journal=Physical Review D | publisher=American Physical Society (APS) | volume=62 | issue=8 | date=2000-09-08 | issn=0556-2821 | doi=10.1103/physrevd.62.084003 | page=084003| arxiv=astro-ph/9904193 | bibcode=2000PhRvD..62h4003V | s2cid=15956589 }} in astronomy and mathematics relates to the angular positions of an unlensed source $\backslash left(\backslash beta\backslash right)$, the image $\backslash left(\backslash theta\backslash right)$, the Einstein bending angle of light $(\backslash hat\{\backslash alpha\})$, and the angular diameter lens-source $\backslash left(D\_\{ds\}\backslash right)$ and observer-source $\backslash left(D\_s\backslash right)$ distances.

:$\backslash tan\; \backslash beta\; =\; \backslash tan\; \backslash theta\; -\; \backslash frac\{D\_\{ds\}\}\{D\_s\}\; \backslash left\; [\backslash tan\; \backslash theta\; +\; \backslash tan\; \backslash left\; (\backslash hat\{\backslash alpha\}-\backslash theta\backslash right\; )\; \backslash right\; ]$.

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