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In this paper, light propagation in a pressure-free non-magnetized plasma onKerr spacetime is considered, which is a continuation of our previous study[Phys. Rev. D 95, 104003 (2017)]. It is assumed throughout that the plasmadensity is of the form that allows for the separability of the Hamilton-Jacobiequation for light rays, i.e., for the existence of a Carter constant. Here wefocus on the analysis of different types of orbits and find several peculiarphenomena which do not exist in the vacuum case. We start with studyingspherical orbits and conical orbits. In particular, it is revealed that in theergoregion in the presence of a plasma there can exist two different sphericallight rays propagating through the same point. Then we study circular orbitsand demonstrate that, contrary to the vacuum case, circular orbits can existoff the equatorial plane in the domain of outer communication of a Kerr blackhole. Necessary and sufficient conditions for that are formulated. We also finda compact equation for circular orbits in the equatorial plane of the Kerrmetric, with several examples developed. Considering the light deflection inthe equatorial plane, we derive a new exact formula for the deflection anglewhich has the advantage of being directly applicable to light rays both insideand outside of the ergoregion. Remarkably, the possibility of a non-monotonicbehavior of the deflection angle as a function of the impact parameter isdemonstrated in the presence of a non-homogeneous plasma. Furthermore, in orderto separate the effects of the black-hole spin from the effects of the plasma,we investigate weak deflection gravitational lensing. We also add some furthercomments to our discussion of the black-hole shadow which was the main topic ofour previous paper.

Light propagation in a plasma on Kerr spacetime. II. Plasma imprint on photon orbits