A comprehensive characterization of the optical properties of wurtzite InN films grown by molecular beam epitaxy on Si(111) substrates is presented. Two types of films are investigated in this work: InN on AlN/Si(111) and InN on GaN/AlN/Si(111). Their properties are compared to a layer deposited on GaN/ sapphire substrate. The dielectric function (DF) is obtained from spectroscopic ellipsometry (SE). The infrared studies yield the plasma frequency and thus the electron density, while the interband absorption is probed between 0.56 and 9.8 eV. For InN grown on Si(111) substrate, the absorption onset is slightly shifted to higher energies with respect to the InN film grown on GaN/sapphire which can be attributed to higher electron concentrations. Despite this, strongly pronounced optical transitions due to critical points of the band structure are found in the high-energy part of the DF. It emphasizes the already promising quality of the InN films on silicon. Band-gap renormalization (BGR), band filling, and strain are taken into account in order to estimate the intrinsic band gap of wurtzite InN. For the InN layers on silicon, we get a band gap between 0.66 and 0.685 eV.