  The influence of the medium on the gravitational deflection of light rays is
widely discussed in literature for the simplest non-trivial case: cold
non-magnetized plasma. In this article, we generalize these studies to the case
of an arbitrary transparent dispersive medium with a given refractive index. We
calculate the deflection angle of light ray moving in a general spherically
symmetric metric in the presence of medium with the spherically symmetric
refractive index. The equation for the radius of circular light orbits is also
derived. We discuss in detail the properties of these results and various
special cases. In particular, we show that multiplying the refractive index by
a constant does not affect the deflection angle and radius of circular orbits.
At the same time, the presence of dispersion makes the trajectories different
from the case of vacuum even in spatially homogeneous medium. As one of the
applications of our results, we calculate the correction to the angle of vacuum
gravitational deflection for the case when a massive object is surrounded by
homogeneous but dispersive medium. As another application, we present the
calculation of the shadow of a black hole surrounded by medium with arbitrary
refractive index. Our results can serve as a basis for studies of various
plasma models beyond the cold plasma case.
