Diffraction of Plane Radio Waves by a Parabolic Cylinder

A number of investigators have studied the effect of hills on the propagation of short radio waves. Experiment has shown that the field far behind a hill may be computed, to a reasonable degree of accuracy, by assuming that the hill acts like a knife-edge (half-plane)1. The question naturally arises as to the conditions under which such an assumption is permissible. Here we attempt to throw some light on this question by taking the hill to be a parabolic cylinder. Our results indicate that, for small angles of diffraction, even gently curved hills act like knife-edges. However, for larger angles corresponding to points deep in the shadow or to points high in the illuminated region, it may be necessary to use the more exact formulas which take the curvature of the hill into account. 1 See, for example, Ultra-Short-Wave P r o p a g a t i o n , J. C. Schelleng, C. R. Burrows a n d E. B. Ferrell, Proc. I . R . E . , 21, p p . 423-463, 1933.