Аннотация:Based on the mathematical analysis of the solution of the system of Maxwell equations for the boundary value problem of excitation of a nonlocal scatterer located near a transparent substrate by an electric dipole of arbitrary polarization, a universal formula for the extinction cross-section is obtained. The formula permits one to determine the extinction crosssection by calculating the scattered field at a single point. The result is generalized to the case of excitation of a scatterer by a multipole of arbitrary order in the presence of a transparent substrate; in this case, the multipole can be located both near the scatterer and inside the substrate. Based on the studies carried out, a formula for calculating the fluorescence quantum yield is obtained that eliminates the need to calculate the absorption cross-section for a scattererwith a nonlocality effect.