Ultrathin anthracene layers, UHV-deposited on He-cooled inorganic single crystal substrates (Cu, Ag, Si, KCl) were studied in situ by ps time-resolved fluorescence techniques. The dependencies of both fluorescence spectra and transients on anthracene coverage (mono/multilayers with thicknesses d = 3.5-1000 Angstrom) and sample temperature (T = 10-300 K) were measured. The distance dependent interaction between electronically excited anthracene and the substrate results in fluorescence quenching, which can be described by applying a modified classical image dipole theory. The dependence of the quenching efficiency on the dielectric function of the substrate is verified. The competing dispersive energy transfer within the anthracene layers could be separated and quantified.