Van Siclen (1988 Am. J. Phys. 56 1142) reported a curious property of a dielectric sphere in the field of an external point charge: the field outside the sphere generated by the combination of the original charge exterior and the Kelvin image charge interior to the sphere is independent of the permittivity of the sphere. In this paper,we simplify and correct the original derivation and give a detailed analysis of the sources of the field. We also present various checks for the theory, providing instructive exercises for advanced undergraduates.