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Alec Aivazis added grav lense.tex
almost 10 years ago
Commit id: 891980020aaf9a6bdbef1056c3e23180ed45d672
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\section{Grav Lenses}
Diagram is in figure \ref{fig:gravlense}.
\begin{equation}
\theta D_{S} = \beta D_S + \alpha D_{LS}
\end{equation}
Because $b \approx \xi$ and $\xi \approx \theta D_L$ we can use the small angle approx. Therefore, $\theta = \beta + \frac{\theta_{E}^2}{\theta}$. Where
\begin{equation}
\theta_E = \left[ 2 R_S \frac{D_{LS}}{D_{S}D_{L}} \right] ^\frac{1}{2}
\end{equation}
