Snell's law and walking droplets

Droplets walking on the surface of a vibrating bath have been shown to exhibit a number of quantum-like features. We here present the results of a combined experimental and theoretical investigation of such droplets crossing a linear step corresponding to a reduction in bath depth. When the step is sufficiently large, the walker reflects off the step; otherwise, it is refracted as it crosses the step. Particular attention is given to an examination of the regime in which the droplet obeys a form of Snell's Law, a behavior captured in accompanying simulations. Attempts to provide theoretical rationale for the dependence of the effective refractive index on the system parameters are described.