In this paper we first recall the Morse relations for Light rays in vacuum.
They can be obtained, under quite general assumptions, by the relativistic
Fermat principle stated by Kovner and correctly proved by Perlick. They ca
n be used for a global mathematical description of the gravitational lens e
ffect. Afterwards we consider the well known thin lens model and we observe
that the light rays having a geometrical index equal to 2 have a strong co
nstraint about the surface density where they pass the deflector. Finally,
we note that in situations similar, for example, to the Einstein cross (who
se models predict the existence of one light ray having its geometrical ind
ex equal to 2), the constraint on the surface density suggests that the abs
orption may be so high that the related image is quite difficult to detect.