= Singular isothermal sphere lens
{title2=$\theta_E=4\pi(\sigma/c)^2D_{ds}/D_s$}
The projected density $\Sigma(R)=\sigma^2/(2GR)$ gives cylindrical mass $\pi\sigma^2R/G$, so the reduced deflection magnitude is the constant displayed angular <Einstein radius>. The signed <thin gravitational lens equation> is $\beta=\theta-\theta_E\operatorname{sgn}\theta$. A source with $0<\beta<\theta_E$ has two images; one with $\beta>\theta_E$ has one. The <lensing convergence> and <lensing shear> magnitude are both $\theta_E/(2|\theta|)$.
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