A generalized lens equation for light deflection in weak gravitational fields

A generalized lens equation for weak gravitational fields of Schwarzschild metric and valid for finite distances of source and observer from the light deflecting body is suggested. The magnitude of neglected terms in the generalized lens equation is estimated to be smaller than or equal to (15π)/4 (m2)/d'2, where m is the Schwarzschild radius of the massive body and d ' is Chandrasekhar's impact parameter. The main applications of this generalized lens equation are extreme astrometrical configurations, where the standard post-Newtonian approach as well as the classical lens equation cannot be applied. It is shown that in the appropriate limits, the proposed lens equation yields the known post-Newtonian terms, 'enhanced' post-post-Newtonian terms and the classical lens equation, thus providing a link between both these essential approaches for determining the light deflection.