  We have analyzed the observed image separations of the gravitationally lensed
images of QSOs for a possible correlation with the source redshift. Contrary to
the previously noted anti-correlation based on a smaller data set, no
correlation is found for the currently available data. We have calculated the
average image separations of the lensed QSOs as a function of source redshifts,
for isothermal spheres with cores in a flat universe, taking into account the
amplification bias caused by lensing. The shape of the distribution of average
image separation as a function of redshift is very robust and is insensitive to
most model parameters. Observations are found to be roughly consistent with the
theoretical results for models which assume the lens distribution to be (i)
Schechter luminosity function which, however, can not produce images with large
separation and (ii) the mass condensations in a cold dark matter universe, as
given by the Press-Schechter theory if an upper limit of 1-7$\times 10^{13}$
M$\odot$ is assumed on the mass of the condensations.

Astrophysics