  We discuss the ratio of the angular diameter distances from the source to the
lens, $D_{ds}$, and to the observer at present, $D_{s}$, for various dark
energy models. It is well known that the difference of $D_s$s between the
models is apparent and this quantity is used for the analysis of Type Ia
supernovae. However we investigate the difference between the ratio of the
angular diameter distances for a cosmological constant,
$(D_{ds}/D_{s})^{\Lambda}$ and that for other dark energy models,
$(D_{ds}/D_{s})^{\rm{other}}$ in this paper. It has been known that there is
lens model degeneracy in using strong gravitational lensing. Thus, we
investigate the model independent observable quantity, Einstein radius
($\theta_E$), which is proportional to both $D_{ds}/D_s$ and velocity
dispersion squared, $\sigma_v^2$. $D_{ds}/D_s$ values depend on the parameters
of each dark energy model individually. However, $(D_{ds}/D_s)^{\Lambda} -
(D_{ds}/D_{s})^{\rm{other}}$ for the various dark energy models, is well within
the error of $\sigma_v$ for most of the parameter spaces of the dark energy
models. Thus, a single strong gravitational lensing by use of the Einstein
radius may not be a proper method to investigate the property of dark energy.
However, better understanding to the mass profile of clusters in the future or
other methods related to arc statistics rather than the distances may be used
for constraints on dark energy.
