  In this paper we study the motion of photons or massless particles in the
C-metric with cosmological constant. The Hamilton--Jacobi equations are known
to be completely separable, giving a Carter-like quantity $Q$ which is a
constant of motion. All possible trajectories are classified according to a
two-dimensional parameter space representing the particle's angular momentum
and energy scaled in units of $Q$. Exact solutions are given in the C-metric
coordinates in terms of Jacobi elliptic functions. Using the exact solutions,
we find examples of periodic orbits on the photon surface.
