Approximation of light-ray deflection angle and gravitational lenses in the Schwarzschild metric.: II.: Lensing magnification in a binary system

We apply an exact solution of a light deflection angle in the Schwarzschild metric, written with elliptic integrals, to the basic lensing theory. The magnifications for a point and a surface source are calculated and compared to the magnification provided by the usually applied traditional Einstein solution. We propose a simple correction to the Einstein angle 4/b that fixes it closer to the solution written with an elliptic integral. The results are applied to an eclipsing binary system, and the luminosity of a binary system at the secondary eclipse with lensing effects is calculated. Our results show that the radius of the Einstein ring, where the magnification diverges, is slightly underestimated by the Einstein solution. This leads to an error of the overall brightness of a point-mass lens. The effect is pronounced with systems of comparable physical and Einstein radii, especially when the Einstein ring is partially inside the physical radius of the lens object. The difference is not usually large, but in the worst case of a tight double neutron star, the error made in total flux can be on the order of 10% if the higher order effects are neglected.