The method of attenuated total internal reflection has been used in the visible region to obtain precise values of the dielectric function of Ag films in contact with different dielectric media. By measuring, at eight visible laser wavelengths, the surface-plasmon resonance of an Ag film against air and then against an organic liquid, we show that for both cases the dielectric function can be described by the Drude model with the well-known frequency-dependent relaxation time, namely,-1()=0-1+2. The interesting results are that 0-1(liquid)>0-1(air), that (liquid)<(air), and that the plasma frequency p(liquid)>p(air). The fact that changes the sign of the change or its magnitude appears to eliminate all previous models which have been proposed to describe this frequency-dependent term. The observed changes in and p are consistent with the idea of a complex relaxation time whose real and imaginary parts are connected in a causal way. The index-of-refraction dependence of the Drude parameters demonstrates that surface electrodynamics must play an important role. The observed trends reported here could be accounted for if increasing the index of the dielectric half-space would increase the attractive surface-plasmon interaction and decrease the magnitude of electron-electron scattering in the Ag surface. © 1984 The American Physical Society.