Focusing equations, caustics and the condition for multiple imaging by thick gravitational lenses

Abstract

The condition for the production of multiple images by an arbitrary (thick or thin) gravitational lens are studied. We show that the necessary and sufficient condition for the production of multiple images by a lens is the following: The lens should produce a point conjugate to the observer, along some null geodesic, at an affine distance smaller than that of the source. It is shown that previous results on multiple imaging by thin lenses can be obtained as a special case. We also show that a thick lens cannot be more efficient than a suitably designed thin lens for the production of multiple images.