The path, the size and the cross section of a light bundle
propagating through spacetime in principle are affected by all
the matter between the light source and the observer. For most
practical purposes, we can assume that the lensing action is
dominated by a single matter inhomogeneity at some location
between source and observer. This is usually called the ``thin
lens approximation'': All the action of deflection is thought to
take place at a single distance. This approach is valid only if
the relative velocities of lens, source and observer are small
compared to the velocity of light
and if the Newtonian potential is small
. These two assumptions are justified in all astronomical cases
of interest. The size of a galaxy, e.g., is of order 50 kpc, even
a cluster of galaxies is not much larger than 1 Mpc. This ``lens
thickness'' is small compared to the typical distances of order
few Gpc between observer and lens or lens and background
quasar/galaxy, respectively. We assume that the underlying
spacetime is well described by a perturbed
Friedmann-Robertson-Walker metric
: