We have measured the nuclear transparency of the incoherent diffractive
$A(e,e'\rho^0)$ process in $^{12}$C and $^{56}$Fe targets relative to $^2$H
using a 5 GeV electron beam. The nuclear transparency, the ratio of the
produced $\rho^0$'s on a nucleus relative to deuterium, which is sensitive to
$\rho A$ interaction, was studied as function of the coherence length ($l_c$),
a lifetime of the hadronic fluctuation of the virtual photon, and the
four-momentum transfer squared ($Q^2$). While the transparency for both
$^{12}$C and $^{56}$Fe showed no $l_c$ dependence, a significant $Q^2$
dependence was measured, which is consistent with calculations that included
the color transparency effects.
