In order to study the optical characteristics of silicon at different temperatures, a general Cauchy dispersion equation for Silicon material that depends on temperature and wavelength was derived in this paper. The wavelengths vary between 1.2 and 14 µm, and the temperatures vary from 100 to750K. There was a great deal of agreement between the computed refractive index of three digits and previously published data. In addition, the phase velocity for the waves in the material was measured and, when compared to actual values, The results demonstrated good concordance.