BEYOND THE THIN LENS APPROXIMATION

We obtain analytic formulae for the null geodesics of Friedmann-Lemait re-Robertson-Walker spacetimes with scalar perturbations in the longit udinal gauge. From these we provide a rigorous derivation of the cosmo logical lens equation and obtain an expression for the magnification o f a bundle of light rays without restriction to static or thin lens sc enarios. We show how the usual magnification matrix naturally emerges in the appropriate limits.