Impurities are known to affect vibrational properties of crystals by modifying the distribution of normal mode frequencies and altering the nature of the atomic displacements in the neighborhood of the impurities. We have calculated the effects of isotopic impurities on the lattice vibrational optical absorption of both monatomic and diatomic linear chains of alternately charged particles. It is found that even with the harmonic approximation and the use of the cyclic boundary condition, the presence of impurities leads to a broad absorption of the low frequency side of the main maximum. This is in contrast with the delta-function type of absorption at the optical frequency predicted by these models in the absence of impurities. For those cases in which discrete frequencies associated with localized vibrational modes occur, absorption at these isolated frequencies also occurs. This latter absorption can take place at frequencies higher than that of the main maximum. A discussion will be given of the relation between the results of our calculations and available experimental data.