Optical caustics from liquid drops under gravity: observations of the parabolic and symbolic umbilics

Abstract

An earlier paper (Nye 1978) discussed the caustics formed by refraction of light in a thin gravity-free water drop resting on a glass surface. Here the effect of gravity is examined. In an irregular drop clinging to an inclined glass surface all the elementary catastrophes of co-dimension up to three are seen, including the hyperbolic umbilic. By suitably controlling the shape of the drop one can produce the higher-order singularities D₅(parabolic umbilic) and E₆(symbolic umbilic) with their corresponding unfoldings. The local topology of E₆is accompanied by characteristic global topology signifying the presence of a higher organizing centre. Recognizing the typical unfolding patterns of D₅and E₆makes it possible to understand part of the complex pattern of interaction of the caustics from a thin irregular drop under gravity. D₅and E₆are to be expected theoretically when a wave is refracted by a surface which is shaped by the combined effects of surface tension and gravity. The calculated relation between the canonical control parameters of these catastrophes and the physical controls, such as focusing, gives a satisfactory explanation of what is seen. Three examples show how reactions between umbilic points on a variable surface can be related to higher order umbilic catastrophes.