We present the combined experimental and theoretical investigations of the optical properties of amorphous carbon. The reflection electron energy loss spectra (REELS) spectra of carbon were measured using a cylindrical mirror analyzer under ultrahigh vacuum conditions at primary electron energies of 750, 1000 and 1300 eV. The energy loss function and thereby the refractive index n and the extinction coefficient k were determined from these REELS spectra in a wide loss energy range of 2-200 eV by applying our reverse Monte Carlo method. The high accuracy of the obtained optical constants is justified with the ps- and f-sum rules. We found that our present optical constants of amorphous carbon fulfill the sum rules with the highest accuracy compared with the previously published data. Therefore, we highly recommend to replace the previous data with the present ones for practical applications. Moreover, we present the atomic scattering factors of amorphous carbon obtained from the dielectric function to predict its optical constants at a given density.