  We construct a semi-microscopic theory, to describe the optical conductivity
of GaMnAs in the dilute limit, x = 1%. We construct an effective Hamiltonian
that captures inside-impurity band optical transitions as well as transitions
between the valence band and the impurity band. All parameters of the
Hamiltonian are computed from microscopic variational calculations. We find a
metal-insulator transition within the impurity band in the concentration range,
x = 0.2 -0.3 for uncompensated and x = 1-3% for compensated samples, in good
agreement with the experiments. We find an optical mass m_opt = m_e, which is
almost independent of the impurity concentration excepting in the vicinity of
the metal-insulator transition, where it reaches values as large as m_opt = 10
m_e. We also reproduce a mid-infrared peak at \hbar \omega = 200 meV, which
redshifts upon doping, in quantitative agreement with the experiments.
