  It is shown that polarization transfer measurements $(\vec{e},e'\vec{p})$ on
a specific target nucleus can provide constraints on the ratio of the in-medium
electric to magnetic form factor. Thereby one exploits the fact that proton
knockout from single-particle levels exhibit a specific sensitivity to the
effective nuclear density. It is shown that in $^{12}$C the effective nuclear
density for $s$-shell knockout is about twice as high as for $p$-shell
knockout. With current model predictions for the in-medium form factors, one
obtains measurable modifications of the order of 5% in the ratios of the double
polarization observables between those single-particle levels.
