In this work we study theoretically the scattering of p-polarized light of frequency (omega) from a system consisting of a dielectric medium (prism) characterized by a dielectric constant (epsilon) 0 in the region x3 $GTR D; a metal film characterized by a complex, frequency-dependent dielectric function(epsilon) 1((omega) ) in the region 0 < x3 < D; a dielectric film characterized by a dielectric constant (epsilon) 2 in the region (zetz) (x1) < x- 3) < 0; and vacuum ((epsilon) 3 equals 1) in the region x3 < (zetz) (x1). The light whose plane of incidence is the x1x3- plane, in incident through the prism. For the surface profile function (zetz) (x1) we take the form (zetz) (x1) equals -d(theta) (x1)(theta) (L-x(1), where (theta) (x1) is the Heaviside unit step function. Thus we have a dielectric film thickness d and dielectric constant (epsilon) 2 covering the half of the lower surface (x3 equals 0) of the metal film defined by x1$GTR0, or a dielectric film of thickness d and dielectric constant (epsilon) 2 covering the part of the lower surface (x3 equals 0) of the metal film defined by 0 < x1 < L. The reduced Rayleigh equation for the amplitude of the light scattered back into the prism, R(qk), is obtained, and solved by the Wiener-Hopf method, and the result is used to calculate the intensity of the scattered field in the far field region as a function of x1 for a fixed value of x3 for several values of the wavelength of the incident light. The results provide information about the scattering of the surface plasmon polariton at the metal-vacuum interface, excited by the incident light, by an index step on that interface. A brief discussion of the transmission of light through this system is also given.