Statistics of gravitational lenses: apparent changes in the luminosity function of distant sources due to passage of light through a single galaxy

We ask how the apparent distribution of fluxes (N-F relation) of point sources seen behind an intervening galaxy will change due to gravitational lensing of the galaxy as a whole or due to mini-lenses within it. The analysis is exact in the limit that the optical depth to lensing is small. We find that there should be a significant increase in the apparent density of quasars seen near galaxies but that a sample of more than 10/sup 4,5/ galaxies will have to be studied before a statistically significant result is found. The resulting amplification of the N-F relation depends sensitively on the slope and curvature of the initial N-F relation. Because of this and requirements of flux conservation, there is expected to be a decrement of very faint quasars (m>26.5) seen near galaxies. This, coupled with the scarcity of bright quasars, implies that searches should optimally be made in the vicinity of m = 23. The apparent amplification found by Canizares with a smaller sample (Nroughly-equal10/sup 3,3/) of galaxies using relatively bright quasars (m<16) is, if real and not a statistical anomaly, due to physical effects other than gravitational lensing