We have used high-resolution infrared laser spectroscopy and optothermal detection to investigate the scattering of methane from LiF(100). The angular, translational, and rotational distributions of the scattered molecules are reported as a function of incident energy, surface temperature, and incident angle. The results show structured angular distributions that can be understood in terms of rainbow scattering, providing information on the surface corrugation appropriate to methane, as well as insights into the energy transfer between the methane and the surface. In addition, the energy dependence of the rainbow scattering, together with the rotational distributions, provide insights into the molecular anisotropy at both long and short ranges. The experimental results are compared with those of the washboard model for rainbow scattering [J. C. Tully, J. Chem. Phys. 92, 680 (1990)].