We study the effect of a plane gravitational wave of limited duration ('sandwich wave') on an infinite set of test particles at relative rest. We prove, at least for waves of fixed polarization, that all the particles strung out in a certain direction will collide after a finite time that is independent of how far apart they were originally. This we call the caustic property. The effect of the wave on null geodesics is such that this phenomenon does not require any particle to move faster than light. Indeed, an observer who has passed through such a wave will within a finite time have seen an infinite spatial volume lying in a space-like half-hyperplane on the other side of the wave. For a certain ('bicaustic') type of wave the whole of that half-hyperplane will have become visible.