  We study gravitational lensing with a multiple lens plane approach, proposing
a simple analytical model for the probability distribution function (PDF) of
the dark matter convergence, kappa, for the different lens planes in a given
cosmology as a function of redshift and smoothing angle, theta. The model is
fixed solely by the variance of kappa, which in turn is fixed by the amplitude
of the power spectrum, sigma_8. We test the PDF against a high resolution
Tree-Particle-Mesh simulation and find that it is far superior to the Gaussian
or the lognormal, especially for small values of theta << 1 arcmin and at large
values of kappa relevant to strong lensing. With this model, we predict the
probabilities of strong lensing by a single plane or by multiple planes. We
find that for theta ~ 10 arcsec, a single plane accounts for almost all (~ 98%)
of the strong lensing cases for source redshift unity. However, for a more
typical source redshift of 4, about 12% of the strong lensing cases will result
from the contribution of a secondary clump of matter along the line of sight,
introducing a systematic error in the determination of the surface density of
clusters, typically overestimating it by about 2-5%. We also find that matter
inhomogenieties introduce a dispersion in the value of the angular diameter
distance about its cosmological mean. The probable error relative to the mean
increases with redshift to a value of about 8% for z ~ 6 and theta ~ 10 arcsec.
