  We derive the transmission coefficient, $T(\omega)$, for grazing incidence of
crystals with spatial dispersion accounting for the excitation of multiple
modes with different wave vectors ${\bf k}$ for a given frequency $\omega$. The
generalization of the Fresnel formulas contains the refraction indices of these
modes as determined by the dielectric function $\epsilon(\omega,{\bf k})$. Near
frequencies $\omega_e$, where the group velocity vanishes, $T(\omega)$ depends
also on an additional parameter determined by the crystal microstructure. The
transmission $T$ is significantly suppressed, if one of the excited modes is
decaying into the crystal. We derive these features microscopically for the
Josephson plasma resonance in layered superconductors.
