  The effects on Raychaudhuri's equation of an intrinsically-discrete or
particle nature of spacetime are investigated. This is done through the
consideration of null congruences emerging from, or converging to, a generic
point of spacetime, i.e. in geometric circumstances somehow prototypical of
singularity issues. We do this from an effective point of view, that is through
a (continuous) description of spacetime modified to embody the existence of an
intrinsic discreteness on the small scale, this adding to previous results for
non-null congruences.
  Various expressions for the effective rate of change of expansion are
derived. They in particular provide finite values for the limiting effective
expansion and its rate of variation when approaching the focal point. Further,
this results in a non-vanishing of the limiting cross-sectional area itself of
the congruence.
