In the last few years, infrared reflection-absorption spectroscopy (IRRAS) has become a standard technique to study vibrational excitations of molecules. These investigations are strongly motivated by potential applications in monitoring chemical processes. For a better understanding of the adsorption mechanism of molecules on dielectrics, the polarization-dependence of an interaction of infrared light with adsorbates on dielectric surfaces is commonly used. Thus, the peak positions in absorption spectra could be different for s- and p-polarized light. This shift between the peak positions depends on both the molecule itself and the dielectric substrate. While the origin of this shift is well understood for infinite two-dimensional adsorbate layers, finite-size samples, which consist of 2D islands of a small number of molecules, have never been considered. Here, we present a study on polarization-dependent finite-size effects in the optical response of such islands on dielectric substrates. The study uses a multi-scale modeling approach that connects quantum chemistry calculations with Maxwell scattering simulations. We distinguish the optical response of a single molecule, a finite number of molecules, and a two-dimensional adsorbate layer. We analyze CO and CO2 molecules deposited on CeO2 and Al2O3 substrates. The evolution of the shift between the polarization-dependent absorbance peaks is first studied for a single molecule, which does not exhibit any shifting at all, and for finite molecular islands, where it increases with increasing island size, as well as for an infinite two-dimensional adsorbate layer. In the latter case, the agreement between the obtained results and the experimental IRRAS data and more traditional three/four-layer model theoretical studies supports the predictive power of the multi-scale approach.