Scattering from a foil

  Now imagine a thin foil (thickness t) of a material consisting of these reflectors (still radius 2f) with a density of n reflectors per unit volume. Normally incident on this foil we direct a current of I particles per unit time. The beam spreads over a wide region of the foil as Figure 3.5 shows.

Assume for simplicity that the foil is sufficiently thin and the reflectors sufficiently small compared to their average spacing that that the reflectors do not occult one another and that the vast majority of particles pass through the foil colliding with at most one reflector. What fraction of the particles can be expected to pass through the foil without a single collision? Ignoring multiple scattering events, at what rate (particles/unit time) will particles emerge from the foil with deflection angles less than away from the direction?