  The semi-inclusive deep inelastic scattering of electrons off the deuteron
($^2H \equiv D$) and $^3He$ with detection of slow protons and deuterons,
respectively, i.e. the processes $D(e,e'p)X$ and $^3He(e,e'D)X$, are calculated
within the spectator mechanism, taking into account the final state interaction
of the hadronizing quark with the detected protons and deuterons, respectively.
It is shown that by a proper choice of the kinematics the origin of the EMC
effect and the details of the interaction between the hadronizing quark and the
nuclear medium can be investigated at a level which cannot be reached by
inclusive deep inelastic scattering. A comparison of our calculations with
recently available experimental data on the process $D(e,e'p)X$ shows a good
agreement in the backward hemisphere of the emitted nucleons. Theoretical
predictions at the energies thyat will be available at the upgraded Thomas
Jefferson National Accelerator Facilty are presented, and the possibility to
investigate the proposed semi-inclusive processes at electron-ion colliders is
briefly discussed.
