Time-resolved scanning Kerr microscopy data are presented that illustrate the refraction and total reflection of spin waves in a Ni80Fe20 film at a film-thickness step. In our experiments spin waves are excited with microwaves on coplanar wave guides. By changing the orientation of an externally applied magnetic field, we can manipulate the group velocity of the wave and hence control the angle of incidence on the step. An interface mode bound at the step is observed, when the magnetic field vector is perpendicular to the step. We point out the general conditions under which such interface modes can be expected in media with strongly anisotropic dispersion.