Halliday, Resnick & Walker — Diffraction: Problem 34

34 Babinet’s principle. A monochromatic beam of parallel light is incident on a “collimating” hole of diameter \(x \gg \lambda\). Point \(P\) lies in the geometrical shadow region on a distant screen (Fig. 36-36a). Two diffracting objects, shown in Fig. 36-36b, are placed in turn over the collimating hole. Object \(A\) is an opaque circle with a hole in it, and \(B\) is the “photographic negative” of \(A\). Using superposition concepts, show that the intensity at \(P\) is identical for the two diffracting objects \(A\) and \(B\).