| Summary: | Phase and group velocities of isotropic and anisotropic waves are expressed analytically by the frequency-wave number vector relations and graphically with frequency curves for a multiple-dimensional space. Both velocities are proved to be parallel for isotropic waves, thus leading to a conclusion that a group of isotropic waves are refracted by Snell's law. Superposition of two sine waves lead to the group velocity only when the two waves have the same direction. It is proved wrong to conclude from the superposition method that a group of gravity waves are refracted at a discontinuity by Snell's law with group velocity instead of phase velocity. In Appendix A is treated refraction of a group of two anisotropic waves, the internal gravity waves and the Rossby waves. In Appendix B is presented the mathematical derivation by the proponents of Snell's law with group velocity and their errors are pointed out. (Author).
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