= Thin gravitational lens equation
{title2=$\boldsymbol\beta=\boldsymbol\theta-\boldsymbol\alpha$}
A thin lens maps apparent image angle $\boldsymbol\theta$ to unlensed source angle $\boldsymbol\beta$. In the usual outward reduced-deflection convention, $\boldsymbol\alpha=\nabla_\theta\psi$ for a projected lensing potential. For an axisymmetric lens its magnitude is $4GM_{\rm projected}(<D_d\theta)D_{ds}/(c^2D_dD_s\theta)$. The mass here is projected inside a cylinder, not the three-dimensional mass inside a sphere.
Back to article page