We have made infrared reflectivity measurements on single crystals of La2CuO4 and La1.92Sr0.08CuO4 with the infrared radiation polarized parallel and perpendicular to the copper-oxygen planes. In La2CuO4 we observe nearly insulating spectra, from which we easily identify the dominant in-plane and out-of-plane infrared-active phonons. When La2CuO4 is doped with Sr, we observe a dramatic increase in the electronic contribution to the a-b plane conductivity, which tends to screen the in-plane phonons. In contrast, the out-of-plane response is essentially unchanged by doping. This leads to a conductivity anisotropy which we estimate to be at least 50 to 1 for our La1.92Sr0.08CuO4 crystal. Our observations on single crystals resolve some of the controversies which have arisen over the interpretation of reflectivity measurements on polycrystalline samples. © 1989 The American Physical Society.