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A variational method is presented which is used to calculate the energy appearing in the various diffracted orders set up when a plane wave is incident upon a periodic reflecting surface. Either the first or the second boundary condition can be so treated. A sample problem is worked showing that if the average absolute slope of the reflecting surface is small (segments of surface with large slope may be included) and if the displacement of the surface is not large compared with the wavelength of the incident radiation, the formulation gives results correct to within a few percent. The calculation shows the existence of Wood anomalies; these are discussed in the paper

Variational Method for the Calculation of the Distribution of Energy Reflected from a Periodic Surface. I.