  We demonstrate that optical transparency of any two-dimensional system with a
symmetric electronic spectrum is governed by the fine structure constant and
suggest a simple formula that relates a quasi-particle spectrum to an optical
absorption of such a system. These results are applied to graphene deposited on
a surface of oxidized silicon for which we measure ellipsometric spectra,
extract optical constants of a graphene layer and reconstruct the electronic
dispersion relation near the K point using optical transmission spectra. We
also present spectroscopic ellipsometry analysis of graphene placed on
amorphous quartz substrates and report a pronounced peak in ultraviolet
absorption at 4.6 eV because of a van Hove singularity in graphene's density of
states. The peak is downshifted by 0.5 eV probably due to excitonic effects.
