  For a given source and lens pair, there is a thin on-axis tube-like volume
behind the lens in which the radiation flux from the source is greatly
increased due to gravitational lensing. Any objects (such as dust grains) which
pass through such a thin tube will experience strong bursts of radiation, i.e.,
Extreme Gravitational Lensing Events (EGLE). We study the physics and
statistics of EGLE for the case in which finite source size is more important
than shear. One of the several possible significant astrophysical effects is
investigated with an illustrative calculation.
