We measure the reflectivity of pure and doped polycrystalline La2-xSrxCuO4 in the gap region and up to 40 000 cm-1 (5 eV). For the doped sample we analyze the reflectivity in terms of a superposition of a metallic a-b plane component and a nearly insulating c-axis component with ordinary phonons. This approach removes several unphysical results obtained assuming a homogeneous surface and allows agreement between the measured infrared and dc properties, which has not been previously obtained. This approach further indicates that our infrared gap signature is dominated by the c-axis contribution and insensitive to the gap in the a-b plane. We estimate the c-axis gap to be 2"2kBTc, which is small compared to both the isotropic Bardeen-Cooper-Schrieffer prediction and tunneling measurements. © 1987 The American Physical Society.