The cat’s-eye phenomenon: a mathematical approach

This paper provides a mathematical basis for the well-known cat’s-eye effect appearing on chatoyant gemstones. After reminding the reader of the physical origin of this effect and the conditions for observing it, we introduce all required parameters and some reasonable assumptions in order to simplify the calculations. In fact, we describe the motion of a point located at the apex of the cat’s-eye line in the “main” plane, defined by the directions of the source and the observer and perpendicular to the set of acicular inclusions responsible for the optical phenomenon. These calculations confirm the qualitative cat’s-eye behavior commonly observed in various situations, when the source or the observer moves around the cabochon or when the stone rotates under them.