A solution is found of the dispersion equation for a classical oscilla
tor in the vicinity of a dielectric microsphere in the case of strong
electromagnetic coupling. The solution obtained agrees with the corres
ponding quantum-mechanical solution obtained within the framework of t
he dressed states approach and presents a clear signature of the vacuu
m Rabi splitting of the energy levels in real systems. Based on this s
olution, a qualitative expression is found for the intensity of the re
sultant line doublet.