Refractionofshallow-waterwavesovervariablebathymetryistypicallytreatedinoceanog- raphy via the continuous Snell law or by numerical ray tracing. We show that the same physics admits a compact differential-geometric formulation: rays are geodesics of a two- dimensional optical metric. Starting from Fermat’s principle with n = 1/√gh, we derive the explicit Christoffel symbols, recover the Snell invariant, obtain a closed-form ray tra- jectory on a plane beach, and compute the Gaussian curvature of the optical metric, which controlsfocusingthroughthegeodesicdeviationequation. Whilestandardinopticsandrel- ativity, this formalism is rarely used in coastal wave theory and offers a unifying theoretical language.