The Cherenkov light generated by an extensive air shower carries fundamental information on the primary particle. In particular, the radial distribution of Cherenkov light at ground level can be used for the separation of gamma-ray and proton showers. In this paper, the capability of several gamma/proton separation methods in the energy range 1 TeV-10 PeV at several observation levels ranging from 600 g cm^-2 up to sea level are analysed by means of a Monte Carlo simulation. The relation between physical parameters of the shower (e.g. shower maximum depth and electron number at the shower maximum) and the features of the radial distribution of Cherenkov light is studied in detail. First we study the light-electron-slope (LES) method which is based on the measure of the shower size N_e and the slope of the radial distribution of Cherenkov light _c(r) at a distance lower than the hump position. In contrast, two methods relying on the slope of _c(r) beyond the hump are studied; the only-light method which relies in the simultaneous determination of the _c(r) slope both before and beyond the hump and the outer LES method which is based on the measure of N_e and the _c(r) slope beyond the hump. The latter is proposed for the first time in this paper. The dependence of the capabilities of these methods on primary energy and observation altitude is discussed.