The excitation of a perfectly conducting half-plane by a dipole field

Starting with the solution of two scalar problems in diffraction theory derived by MacDonald in 1915, it is shown that the following problem may be solved. An electric or magnetic dipole is situated in the presence of a semi-infinite, perfectly conducting, thin plane. This problem may be solved by appealing to an appropriate representation of the electromagnetic field. When the formulation is complete, we are left merely with a two-dimensional Poisson equation. The method serves to show why some orientations of the dipole are simpler to handle than others.