  The C-metric is a solution to Einstein's vacuum field equation that describes
an accelerating black hole. In this paper we discuss the propagation of light
rays and the resulting lensing features in this metric. We first solve the
lightlike geodesic equation using elliptic integrals and Jacobi elliptic
functions. Then we fix a static observer in the region of outer communication
of the C-metric and introduce an orthonormal tetrad to parameterise the
directions of the light rays ending at the position of the observer using
latitude-longitude coordinates on the observer's celestial sphere. In this
parameterisation we rederive the angular radius of the shadow, we formulate a
lens equation, and we derive the redshift and the travel time of light rays. We
discuss the relevance of our theoretical results for detecting accelerating
black holes described by the C-metric and for distinguishing them from
non-accelerating black holes.
