It is shown how the same physically appealing method can be applied to find analytic solutions for two difficult and apparently unrelated problems in optics and electrostatics. They are: (i) the diffraction of a plane wave at a perfectly conducting thin half-plane and (ii) the electrostatic field associated with a parallel array of stripes held at opposite potentials and lying in a half-plane. In the latter case, the solution of the problem is essential in order to calculate the electron optical phase shift experienced by the electron beam in electron microscopy experiments, where the model mimics an array of reverse biased p-n junctions. This paper is intended, in particular, for the undergraduate student who has completed his programme of calculus and electromagnetism, but it can also be of interest to the general physicist. (Contains 2 figures.)