In condensed matter physics the quasi two-dimensional electron gas at the interface of two different insulators, polar LaAlO3 on nonpolar SrTiO3 (LaAlO3/SrTiO3) is a spectacular and surprising observation. This phenomenon is LaAlO3 film thickness dependent and may be explained by the polarization catastrophe model, in which a charge transfer of 0.5e(-) from the LaAlO3 film into the LaAlO3/SrTiO3 interface is expected. Here we show that in conducting samples (≥4 unit cells of LaAlO3) there is indeed a ~0.5e(-) transfer from LaAlO3 into the LaAlO3/SrTiO3 interface by studying the optical conductivity in a broad energy range (0.5-35 eV). Surprisingly, in insulating samples (≤3 unit cells of LaAlO3) a redistribution of charges within the polar LaAlO3 sublayers (from AlO2 to LaO) as large as ~0.5e(-) is observed, with no charge transfer into the interface. Hence, our results reveal the different mechanisms for the polarization catastrophe compensation in insulating and conducting LaAlO3/SrTiO3 interfaces.