The development of singular amplitudes, or caustics, in the propagation of a high frequency initially plane wave in a three-dimensional homogeneous and isotropic random medium with small (order O(h)) fluctuations in the index of refraction is investigated using geometrical optics. Under a suitable scale, it is proven that, as a function of t, the probability density of distance to first caustic as h tends to zero, is a universal curve, and thus does not depend on the random characteristics of the medium.