of the RICH detector. is a measure of the optical response of the RICH; it can be thought of as the limiting case of the number of actually detected photons produced by a particle whose velocity approaches that of light, averaged over all relevant particle trajectories in the RICH detector. The average number of Cherenkov photons detected, for a slower particle, of charge (normally ±1), emitting photons at angle is then and the precision with which the mean Cherenkov angle can be determined with these photons is approximately to which the angular precision of the emitting particle's measured direction must be added in quadrature, if it is not negligible compared to . Given the known momentum of the emitting particle and the refractive index of the radiator, the expected Cherenkov angle for each particle type can be predicted, and its difference from the observed mean Cherenkov angle calculated. Dividing this difference by then gives a measure of the 'number of sigma' deviation of the hypothesis from the observation, which can be used in computing a probability or likelihood for each possible hypothesis. The following figure shows the 'number of sigma' deviation of the kaon hypothesis from a true pion ring image (π not k) and of the pion hypothesis from a true kaon ring image (k not π), as a function of momentum, for a RICH with = 1.0005, = 25, = 0.64 milliradians; Also shown are the average number of detected photons from pions(Ngπ) or from kaons(Ngk). One can see that the RICH's ability to separate the two particle types exceeds 4-sigma everywhere between threshold and 80 GeV/c, finally dropping below 3-sigma at about 100 GeV. It is important to note that this result is for an 'ideal' detector, with homogeneous acceptance and efficiency, normal error distributions and zero background. No such detector exists, of course, and in a real experiment much more sophisticated procedures are actually used to account for those effects; position dependent acceptance and efficiency; non-Gaussian error distributions; non negligible and variable event-dependent backgrounds. In practice, for the multi-particle final states produced in a typical collider experiment, separation of kaons from other final state hadrons, mainly pions, is the most important purpose of the RICH. In that context the two most vital RICH functions, which maximise signal and minimise combinatorial backgrounds, are its ability to correctly identify a kaon as a kaon and its ability not