The Gravitational Lens Equation for Embedded Lenses; Magnification and Ellipticity

We give the lens equation for light deflections caused by point mass condensations in an otherwise spatially homogeneous and flat universe. We assume the signal from a distant source is deflected by a single condensation before it reaches the observer. We call this deflector an embedded lens because the deflecting mass is part of the mean density. The embedded lens equation differs from the conventional lens equation because the deflector mass is not simply an addition to the cosmic mean. We prescribe an iteration scheme to solve this new lens equation and use it to compare our results with standard linear lensing theory. We also compute analytic expressions for the lowest order corrections to image amplifications and distortions caused by incorporating the lensing mass into the mean.