  We use ray-tracing through the Millennium simulation to study how secondary
matter structures along the line-of-sight and the stellar mass in galaxies
affect strong cluster lensing, in particular the cross-section for giant arcs.
Furthermore, we investigate the distribution of the cluster Einstein radii and
the radial distribution of giant arcs. We find that additional structures along
the line-of-sight increase the strong-lensing optical depth by ~10-25%, while
strong-lensing cross-sections of individual clusters are frequently boosted by
as much as ~50%. The enhancement is mainly due to structures that are not
correlated with the lens. Cluster galaxies increase the strong-lensing optical
depth by up to a factor of 2, while interloping galaxies are not significant.
We conclude that these effects need to be taken into account for predictions of
the giant arc abundance, but they are not large enough to fully account for the
reported discrepancy between predicted and observed abundances. Furthermore, we
find that Einstein radii defined via the area enclosed by the critical curve
are 10-30% larger than those defined via radial surface mass density profiles.
The contributions of radial and tangential arcs to the radial distribution of
arcs can be clearly distinguished. The radial distribution of tangential arcs
is very broad and extends out to several Einstein radii. Thus, individual arcs
are not well suited for constraining Einstein radii.
