Theoretical calculations have shown that in order to obtain changes in the spectrum of light scattered from a randomly rough surface that are large enough to be observed experimentally, this spectrum should be measured at angles of scattering in the near vicinity of features in the scattering pattern whose angular positions depend strongly on the frequency of the incident light. A scattering system that possessses such features is a dielectric film deposited on the planar surface of a reflecting substrate whose illuminated surface is a 2D randomly rough surface. When the dielectric surface is weakly rough, coherent light scattered from this system consists of speckle spots that arrange themselves into concentric interference rings, called Selenyi rings, centered at the normal to the mean surfaces. The angular positions of these rings (intensity maxima) are independent of the angle of incidence of the incident light. When the dielectric surface is strongly rough the angular positions of these rings now depend on the angle of incidence, and they are called Quetelet rings. The angular positions of both types of rings depend strongly on the wavelength of the incident light. Therefore, the spectrum of the scattered light, measured at a scattering angle close to the position of one of these rings, can differ significantly from that of the incident light. In this paper we study experimentally the scattering of light from the system just described, namely a dielectric film deposited on the planar surface of a metallic substrate, when the illuminated surface of the film is a 2D randomly rough surface. We find large changes in the spectrum of the scattered light at scattering angles in the neighborhood of the fringes in the scattering pattern to which this system gives rise.