AN ATTEMPT TO EMPIRICALLY EVALUATE THE GRAVITATIONAL DEFLECTION OF LIGHT IN THE MODIFIED NEWTONIAN DYNAMICS

The deflection angle Delta phi of light rays by the gravitational fiel d of a spherical system M(r) is empirically evaluated using the MOdifi ed Newtonian Dynamics (MOND). It is shown that Delta phi with an impac t parameter r(0) can be expressed by the measured rotation velocity v( r) as Delta phi(r(0)) = 2 integral(r0)(infinity) v(2)(r)/c(2) r(0)dr/r root r(2) - r(0)(2), where [GRAPHICS] and r(c) is the critical radius that is determined by the critical acceleration a(0). In the Newtonia n limit of the gravitational acceleration a much greater than a(0), De lta phi approaches Delta phi = 2Gm(r(0))/c(2)r(0) with the projected s urface mass m(r(0)). Whilst the asymptotic value of Delta phi reaches a constant pi(v infinity/c)(2) in the low-acceleration limit of a much less than a(0). Taking the conventional correction of a factor of 2 f rom the theory of general relativity into account and utilizing the re lation between rotation velocity v and velocity dispersion sigma, MOND results naturally in a constant deflection, 4 pi(sigma/c)(2), which h as been widely used in the present-day study of gravitational lensing by galaxies and clusters of galaxies, implying that without introducin g the massive halos acting as r(-2) for dark matter MOND has no diffic ulty in reproducing the known cases of gravitational lensing associate d with galaxies and clusters of galaxies.