We have applied reflectance anisotropy spectroscopy (RAS) to investigate the rebonded-step (RS) reconstructed strained Ge/Si(105) surface. RAS spectra display a marked peak at 2.1eV that is completely cancelled after exposure to about 1200L of molecular oxygen. Ab initio calculations of the RAS signal explain the experimental spectra in terms of optical transitions between filled bulk-like states and empty surface bands. The early stages of exposure of the clean surface to molecular oxygen have been monitored by RAS and scanning tunneling microscopy (STM), correlating the evolution of the optical anisotropy to the bonding configuration of the adsorbed gas. Oxygen atoms are proposed to first adsorb onto the arms and later on the head dimers ...