The radiation from an electric or magnetic dipole located on the symmetry a
xis of an isorefractive body of revolution (BOR) and axially oriented is co
nsidered, The boundary-value problem is solved exactly for three BOR's: the
isorefractive prolate and oblate spheroids and the isorefractive paraboloi
d. Furthermore, for the isorefractive circular cone, the radiation from an
arbitrarily located and radially oriented dipole, and the scattering from a
n obliquely incident plane wave are determined exactly.