A bare multipole potential Φ(r)=(A/rl+1)Pl(cos θ), concentric with a spherical cavity embedded within a dielectric, has its potential within the dielectric changed, not by the factor ε−1, but rather by the factorF(l)=(2l+1)/[l+(l+1)ε]. Moreover, a multipole source potential in the dielectric Φ(r)=(Arl)Pl(cos θ) has its potential within a concentric spherical cavity changed by a factor εF(l). The result is that the interaction between two multipoles in widely separated cavities is modified by a factor ε−1times a factor εF(l) for each multipole. By decomposing the bare potential of a point monopole source into its cavity multipole components, screening each component separately, and then resumming, it is shown why the method of images works both for point charges with semi‐infinite dielectrics and for line charges with dielectric circular cylinders—butnotfor point changes with dielectric spheres.