A thin cylinder above a finitely conducting half‐space is illuminated by a monochromatic plane wave. The electric vector of the incident plane wave is parallel to the axis of the cylinder and the Poynting vector of this incident plane wave intersects the surface of the finitely conducting half‐space at an oblique angle. An imperfect image is used to derive the total current on the thin cylinder and the electric field at the surface of the half‐space. The total induced current on the thin cylinder is shown to reduce to the appropriate limiting form when the height or the half‐space conductivity becomes infinite.