  The diffraction and transition radiation under normal incidence of a particle
to the semi-infinite dielectric plate had been considered previously using the
eikonal approximation in the transition radiation theory. This approach is
valid for the high radiation frequencies domain (where the dielectric
permittivity of the plate material is close to unit), including X-ray domain.
In the present report this method is applied to the case of oblique incidence
of the particle on the plate (but parallel to the plate's edge) as well as to
the periodic set of such plates (Smith-Purcell radiation). The oblique
incidence of the particle (both in the case of the single plate and in the case
of the periodic grating of such plates) leads to the so called conical effect
in the radiation angular distribution observed recently. We outline that the
origin of this effect lies in the superluminal motion along the plate's edge of
the disturbance produced by the incident particle's field in the plates. The
analogous effects arise in various physical situations. Also we compare our
results to ones obtained using different technique.
