Far-infrared absorption spectroscopy in magnetic fields of up to 30 T of the zinc acceptor impurity in indium phosphide has revealed for the first time a series of free-hole transitions ͑Landau-related series͒ in addition to the familiar bound-hole transitions ͑Lyman series͒ as well as hitherto unobserved phonon replicas of both series. Analysis of these data permits the simultaneous direct experimental determination of ͑i͒ the hole effective mass, ͑ii͒ the species-specific binding energy of the acceptor impurity, ͑iii͒ the absolute energy levels of the acceptor excited states of both odd and even parity, ͑iv͒ more reliable, and in some cases the only, g factors for acceptor states, through relaxation of the selection rules for phonon replicas, and ͑v͒ the LO phonon energy. The method is applicable to other semiconductors and may lead to the reappraisal of their physical parameters.