We present a theory that should explain the operation of the apertureless near‐field optical microscope in the limit of smooth variations of both the refractive index and the corrugation of the object. Special emphasis is made on ultimate resolution and the recent experiments by F. Zenhausern, M. P. O’Boyle, and K.H. Wickramasinghe [Appl. Phys. Lett.65, 1623 (1994)]. We show that, in order to obtain resolution better than 7 nm, the variation of the object refractive index has to satisfy severe conditions. ©1995 American Institute of Physics.