  In this paper, light propagation in a pressure-free non-magnetized plasma on
Kerr spacetime is considered, which is a continuation of our previous study
[Phys. Rev. D 95, 104003 (2017)]. It is assumed throughout that the plasma
density is of the form that allows for the separability of the Hamilton-Jacobi
equation for light rays, i.e., for the existence of a Carter constant. Here we
focus on the analysis of different types of orbits and find several peculiar
phenomena which do not exist in the vacuum case. We start with studying
spherical orbits and conical orbits. In particular, it is revealed that in the
ergoregion in the presence of a plasma there can exist two different spherical
light rays propagating through the same point. Then we study circular orbits
and demonstrate that, contrary to the vacuum case, circular orbits can exist
off the equatorial plane in the domain of outer communication of a Kerr black
hole. Necessary and sufficient conditions for that are formulated. We also find
a compact equation for circular orbits in the equatorial plane of the Kerr
metric, with several examples developed. Considering the light deflection in
the equatorial plane, we derive a new exact formula for the deflection angle
which has the advantage of being directly applicable to light rays both inside
and outside of the ergoregion. Remarkably, the possibility of a non-monotonic
behavior of the deflection angle as a function of the impact parameter is
demonstrated in the presence of a non-homogeneous plasma. Furthermore, in order
to separate the effects of the black-hole spin from the effects of the plasma,
we investigate weak deflection gravitational lensing. We also add some further
comments to our discussion of the black-hole shadow which was the main topic of
our previous paper.
