What is Babinet’s principle?

Babinet’s principle is a statement concerning the equivalence of two problems: the solution to one problem gives the solution to the other problem without further effort. This principle is a rigorous result for scattering by thin screens but Babinet had in mind problems where a finite scatterer (such as a sphere) is replaced by its shadow (a thin disc). In general, we no longer have strict equivalence between the two problems, but there are exceptions. The paper reviews what is known (in the context of acoustic and electromagnetic problems), and clarifies the relations between exact results and those obtained using the Kirchhoff approximation and physical-optics approximations.