More on the bending of light !

Abstract

Recently, Rindler and Ishak have argued that the bending of light is, in principle, changed by the presence of a cosmological constant since one must consider not only the null geodesic equation, but also the process of measurement. I agree with the fact that both must be considered. Here, on the basis of the mathematically exact solution to the classical bending problem, and independent of the cosmological constant, I clarify the approximate argument found in the vast majority of texts (new and old) for the measured value of the bending of light for a single source and show that the result is in part due to the almost perfect cancelation of two terms, one of which is seldom considered. When one considers two sources, this cancelation is of no consequence, and, for example, if the sources are opposite with the same associated apsidal distance, the approximate argument gives the rigorously correct answer (up to numerical evaluation), an answer which is unaffected by the presence of a cosmological constant.