Reflection electron energy-loss spectroscopy (REELS) at low energies is very surface sensitive and can be used to characterize the electronic properties of ultrathin films and surface nanostructures. To extract reliable quantitative information from a REELS experiment it is essential to have accurate theoretical algorithms. In this paper, we have studied the validity of a theoretical method proposed by Yubero and Tougaard [Phys. Rev. B 46, 2486 (1992); Phys. Rev B 53, 9719 (1996)] to determine the dielectric function $\ensuremath{\epsilon}$ by using an analysis of an effective experimental REELS cross section determined by the Tougaard--Chorkendorff algorithm [Phys Rev B 35, 6570 (1987)]. To this end, REELS experiments with electrons incident normal to the surface were carried out for a wide range of exit angles (35\ifmmode^\circ\else\textdegree\fi{}--74\ifmmode^\circ\else\textdegree\fi{} to the surface normal) and energies 200, 500, and $1000\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for several materials (Cu, Ag, Au, and Fe). We find that the theory is in very good agreement with experiment for all geometries and energies studied. It is important to note that for a given element, the same $\ensuremath{\epsilon}$ is used for all geometries and energies and that this $\ensuremath{\epsilon}$ is determined by the analysis. The fact that the theory applies at energies at least down to $200\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ where the inelastic mean free path $(\ensuremath{\lambda})$ is $\ensuremath{\sim}0.5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ implies that the method can be used to determine the dielectric properties of nanofilms, and the additional fact that the theory can predict the variation with angle suggests that the method might also be used to determine the dielectric properties of nanostructures.