Reflection and Refraction at a Random Moving Surface I Pattern and Paths of Specular Points

Light falling from a point source on a ruffled surface produces a pattern of images, which move about over the surface. The image points correspond to the maxima, minima, and saddle points of a certain function. It is shown that the images are generally created in pairs, a maximum with a saddle point or a minimum with a saddle point, and that the total numbers of maxima, minima, and saddle points satisfy the relation Nma+Nmi=Nsa+1.The process of creation or annihilation of images is studied in detail, and also the tracks of the image points, in certain special cases. It is shown that closed tracks may be common. This is confirmed by photography of the sea surface.