The basic physics of gravitational lensing depends only a single input from General Relativity, the deflection angle, a, for a light ray passing a mass, M, with an impact
parameter, r:
With the lens geometry shown in Fig. 3.1, we have
4GM riDS
in the small angle approximation. If the lens and source are perfectly aligned, the two images merge to form a ring of radius
known as the Einstein ring radius. (0E is the angular Einstein radius.) We can now rewrite the single lens equation as
i ri _ b and it has two solutions: r+— = 0.5(b ± \Jb2 + 4R2E). The lensed images are also magnified, and the magnification of a source of infinitesimal size can be computed using area elements obtained by differentiating eq. 3.4. This yields
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