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Consider, in the domain of outer communication M+ of a Kerr-Newman black hole, a point p (observation event) and a timelike curve γ (worldline of light source). Assume that γ (i) has no past endpoint, (ii) does not intersect the caustic of the past light cone of p, and (iii) goes neither to the horizon nor to infinity in the past. We prove that then for infinitely many positive integers k there is a past-pointing lightlike geodesic λk of (Morse) index k from p to γ, hence an observer at p sees infinitely many images of γ. Moreover, we demonstrate that all lightlike geodesics from an event to a timelike curve in M+ are confined to a certain spherical shell. Our characterization of this spherical shell shows that in the Kerr-Newman space-time the occurrence of infinitely many images is intimately related to the occurrence of centrifugal-plus-Coriolis force reversal. [ABSTRACT FROM AUTHOR]