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Cherenkov radiation is electromagnetic radiation from a charged particle exceeding the medium's phase velocity: $c/n(\omega )<v<c$. Here $n(\omega )$ is the positive refractive index at angular frequency $\omega$. The threshold uses phase velocity, not group velocity.^[ref]

The beauty of Cherenkov radiation is that uniform motion can generate a sharply directed electromagnetic wave: the medium's response along successive portions of the track adds with matching wave phase on a cone. The moving electric charge drives the medium's electric polarization; the resulting radiation depends on the collective refractive index. This differs from luminescence, where excitation of material is followed by light emission. Both mechanisms can contribute to the same irradiated sample. A visible blue glow alone therefore identifies neither Cherenkov radiation nor a particular radioactive source.

The Cherenkov cone angle turns a measured direction into a constraint on particle speed when the refractive index is known. The Frank-Tamm formula instead predicts the number of emitted photons in a specified wavelength interval. These are complementary observables: the finite-band Cherenkov yield model below shows why both depend on optical dispersion and on which wavelengths are collected. This makes Cherenkov radiation useful for particle detectors, with photon production, transport and detection treated separately.