Propagation of chemical waves in the Belousov-Zhabotinsky reaction in a thin layer of ferroin-loaded cation-exchange resin beads is investigated. Dispersion relations are obtained for waves propagating in layers of resin beads. The relations in layers of resin beads are different both in the trigger wave velocity and the refractory period, when mesh size and/or percentages of cross-linkage of resin beads are different. A system with a sharp boundary between two layers with different wave velocities is made using two different resin beads exhibiting different dispersion relations. Incident waves at any angle from the high-velocity layer are refracted at the boundary. Waves from the low-velocity layer also exhibit refraction when the angle of incidence is smaller than a critical value. Refraction obeys Snell’s law. Incident waves from the low-velocity layer at angles larger than the critical value are reflected. The angle of reflection is equal to the critical angle and does not depend on the incident angle. When the period of incident waves from the high-velocity layer is shorter than the refractory period in the low-velocity layer, wave propagation across the boundary causes the change of frequency.