  We discuss the applicability of the perturbation theory in electrodynamic
problems where the local Leontovich (the impedance) boundary conditions are
used to calculate the ohmic losses at the metallic surface. As an example, we
examine a periodic grating formed from semi- infinite rectangular plates
exposed to the s-polarized electromagnetic wave. Two different ways for
calculation of the ohmic losses are presented: (i) the calculation of the
reflection coefficient obtained with the aid of the perturbation theory (the
impedance is the small parameter) and (ii) the direct calculation of the energy
flux through the metallic surface, when to get the answer only the tangential
magnetic field at the surface of a perfect conductor of the same geometry has
to be known. The results (i) and (ii) differ noticeably. The same difficulty is
inherent in all the problems where the metallic surface has rectangular
grooves. We show that the standard first order perturbation theory is not
applicable since beginning from a number n even the first corrections to the
modal functions ${\phi}_{n}$ used to calculate the fields, are of the same
order as the zero order modal functions (the impedance is equal to zero).
Basing on the energy conservation law we show that the accurate value for the
ohmic losses is obtained with the aid of the approach (ii).
