On the Question of the Solution of the Wave Equation

The problem of normal incidence of a plane wave on a layer with a one‐dimensional perturbation of the permittivity of the medium is considered under the condition that the spatial scale of the inhomogeneity can be both much smaller and on the order of the wavelength in vacuum. An estimate is obtained for the deviation of the solution corresponding to the short‐wavelength approximation from the rigorous solution of the wave equation. The conditions for applying the expression for the field corresponding to the geometric‐optical approach are determined in the case of commensurability of the wavelength and the spatial scale of the inhomogeneity.