We consider a scattering system consisting of a dielectric film deposited on a semi-infinite metal, and focus on the wavelength dependence of the total integrated scattering and angle resolved scattering from such a system. In particular we study theoretically by a large scale rigorous numerical simulation approach the reflectivity, ${\cal R}(\lambda,\theta_0)$, as well as the total scattered energy, ${\cal U}(\lambda,\theta_0)$, of such systems as functions of the wavelength of the incident light and angles of incidence. The scattering system consists of vacuum in the region $x_3 > d_1+\zeta_1 (x_1)$, a dielectric film in the region, $d_2+ \zeta_2 (x_1)< x_3 < d_1+\zeta_1 (x_1)$, and a metal in the region $x_3 < d_2+\zeta_2 (x_1)$. This system is illuminated from the vacuum side by $p$-polarized light whose wavelength is allowed to vary from $0.2 {\rm \mu m}$ to $1.2 {\rm \mu m}$. The film is assumed to have a dielectric function that is insensitive to the wavelength of the incident light. In obtaining the numerical results reported here the metal substrate is taken to be silver. The dielectric function of silver for a given wavelength is obtained by interpolation from experimental values. The surface profile functions, $\zeta_{1,2}(x_1)$, are assumed to be either zero or single-valued functions of $x_1$ that are differentiable as many times as is necessary, and that constitute zero-mean, stationary Gaussian random processes. Their surface height auto-correlation function is characterized by a Gaussian power spectrum. We study and discuss the wavelength dependence (for a few angles of incidence) of ${\cal R}(\lambda,\theta_0)$ and ${\cal U}(\lambda,\theta_0)$ for several scattering systems obtained by turning on and off the surface profile functions $\zeta_{1,2}(x_1)$ and/or the correlation between these two surface profile functions.