Azimuthally directed wave propagation in a concentric cylindrical cavity is considered. The surface impedance of the outer wall is uniform, but there is a discontinuity in the surface impedance for the lower wall. This is a two-dimensional model of propagation of radio waves in the earth-ionosphere waveguide across a land/sea boundary. The dual integral equations for the problem are solved exactly by a Wiener-Hopf procedure. Various limiting forms of the solution are discussed. In particular, it is shown that the exact expression for the mode conversion coefficient is closely related in form to the result obtained by Kirchhoff theory.