The problem of reflection and refraction of elastic waves due to an incident quasi-primary $(qP)$ wave at a plane interface between two dissimilar nematic elastomer half-spaces has been investigated. The expressions for the phase velocities corresponding to primary and secondary waves are given. It is observed that these phase velocities depend on the angle of propagation of the elastic waves. The reflection and refraction coefficients corresponding to the reflected and refracted waves, respectively, are derived by using appropriate boundary conditions. The energy transmission of the reflected and refracted waves is obtained, and the energy ratios and the reflection and refraction coefficients are computed numerically.

The effect of initial stresses on incident quasi SV-waves at a plane interface between two dissimilar pre-stressed elastic half-spaces is investigated. The reflection and refraction coefficients of the reflected and refracted qSV- and qP-waves are derived with the help of appropriate boundary conditions. The coefficients are found to be functions of the angle of incidence and the initial stresses and incremental elastic parameters of the pre-stressed elastic half-spaces.