Clarifying the Optical Thin-lens Equations of Gravitational Self-lensing

Abstract

We exploit an analogy between gravitational lenses and optical lenses to determine the Gaussian form of the optical thin-lens equation of gravitational self-lensing (this is not the deflection-angle equation which is also called the “ray-tracing equation”). As in magnifying glasses, this Gaussian form determines the location of the virtual image in front of the lens and behind the source. Some confusion exists in the literature because a similar-looking equation of totally different substance is often written down, creating the false impression that this may be the equivalent optical lens equation. Although dimensionally correct and quite useful, this imitating form is misleading, as it masks a compound rate that should instead have always been visible. We clarify all related concepts, so that the readers will save themselves the unpleasant experience of reinterpreting/reclassifying the various self-lensing equations, including the new optical forms derived herein.