Astronomy:Virbhadra–Ellis lens equation

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

[math]\displaystyle{ \tan \beta = \tan \theta - \frac{D_{ds}}{D_s} \left [\tan \theta + \tan \left (\hat{\alpha}-\theta\right ) \right ] }[/math].

This lens equation is useful for studying gravitational lensing in a strong gravitational field.