A theory for the optical properties (Raman scattering or I. R. absorption) of crystals containing a small but finite concentration of impurities will be described. One result of this theory will be a qualitative understanding of the various experimental results that have been obtained for different mixed crystals at much larger concentrations. For example, depending on the difference between the impurity atom and the host atom, a single formula describes either the CaF2-SrF2 Raman spectra, in which the Raman frequency shifts linearly with concentration, or the Ge:Si Raman spectra in which new lines appear when Si is added to Ge. The intensity of the new lines increase with increasing Si concentration. The theory further demonstrates that it is possible for the Raman modes and I. R. modes, within the same crystal to vary differently with impurity concentration.