DELPHI barrel RICH operating principle:
The RICH technique consists in both the detection of the presence of Cherenkov light and in the measurement of the Cherenkov angle. With increasing momentum, all Cherenkov angles tend to a common saturated value, theta_sat, independent of particle mass. The saturated angle is given by the relation cos(theta_sat) = 1/n.

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When a particle is in the momentum region where it emits Cherenkov light we speak of "positive identification" or BAND REGION. On the other hand, when the momentum of a particle is below the Cherenkov threshold, we speak of "negative identification" or VETO REGION; also the fact that a particle did not radiate light for a given momentum provides information on its possible flavour. For example, if an hadron (not an electron nor a muon) with a momentum of 5 GeV/c gives light in the gas radiator, it can only have been a pion. The kaons and protons are below the threshold at this momentum. The RICH identification makes use therefore of the information on the particle momentum (coming from the tracking detectors) to calculate the expected Cherenkov angles (or the expected no light emission) for a given particle flavour and to compare this with the measured angle. Probabilities are calculated for each particle mass hypothesis. A charged track emits on average 8 Cherenkov photons in the gas and 12 photons in the liquid.

Why mirrors:
Due to the parabolic shape of the mirrors, the focusing point on the photon detector for photons in the gas radiator does not dependent on the emission point along the particle trajectory.
(Basic geometry: in a parabola, focus is at infinity.)

The RICH detector is designed to let charged tracks traverse a 1 cm thick liquid radiator and a 40 cm thick gas radiator and to detect the emitted Cherenkov photons in a common photon detector.