  We use a high-resolution $N$-body simulation to investigate the influence of
background galaxy properties, including redshift, size, shape and clustering,
on the efficiency of forming giant arcs by gravitational lensing of rich galaxy
clusters. Two large sets of ray-tracing simulations are carried out for 10
massive clusters at two redshifts, i.e. $z_{\rm l} \sim 0.2$ and 0.3. The
virial mass ($M_{\rm vir}$) of the simulated lens clusters at $z\sim0.2$ ranges
from $6.8\times10^{14} h^{-1} {M_{\odot}}$ to $1.1\times 10^{15} h^{-1}
M_{\odot}$. The information of background galaxies brighter than 25 magnitude
in the $I$-band is taken from Cosmological Evolution Survey (COSMOS) imaging
data. Around $1.7\times 10^5$ strong lensing realizations with these images as
background galaxies have been performed for each set. We find that the
efficiency for forming giant arcs for $z_{\rm l}=0.2$ clusters is broadly
consistent with observations. The efficiency of producing giant arcs by rich
clusters is weakly dependent on the source size and clustering. Our principal
finding is that a small proportion ($\sim 1/3$) of galaxies with elongated
shapes (e.g. ellipticity $\epsilon=1-b/a>0.5$) can boost the number of giant
arcs substantially. Compared with recent studies where a uniform ellipticity
distribution from 0 to 0.5 is used for the sources, the adoption of directly
observed shape distribution increases the number of giant arcs by a factor of
$\sim2$. Our results indicate that it is necessary to account for source
information and survey parameters (such as point-spread-function, seeing) to
make correct predictions of giant arcs and further to constrain the
cosmological parameters.(abridged)
