When a charged particle exceeds the phase speed of light c/n in a medium, it emits a coherent blue shock-cone. Slide the speed and index to see the cone form, vanish below threshold, and match the acoustic Mach cone.
A charged particle flies left-to-right through the medium. When v > c/n, overlapping spherical wavefronts pile up into a blue shock-cone — the characteristic Cherenkov glow.
Frank-Tamm: I ∝ (1 − 1/n²β²)/λ² — emission is dominated by short (blue) wavelengths, which is why the glow is blue.
A charged particle moving through a dielectric medium polarizes the surrounding molecules. Each polarization relaxes by emitting a tiny spherical light wavelet. When the particle is slow, these wavelets interfere destructively and nothing propagates outward. But when the particle speed v exceeds the phase speed of light in the medium, c/n, the wavelets can no longer keep up: they pile up into a coherent two-dimensional shock front — a cone of light trailing the particle. The cone half-angle satisfies cos θ = c/(nv) = 1/(nβ). The effect was predicted by Oliver Heaviside (1888) and Sommerfeld, and observed by Pavel Cherenkov (1934); the quantum explanation by Tamm and Frank earned the 1958 Nobel Prize. It is the electromagnetic analogue of a sonic boom.
A supersonic aircraft pushes air molecules aside faster than sound can carry the disturbance away. The overlapping spherical sound waves form a shock cone with half-angle μ satisfying sin μ = c_s/v = 1/Ma, where Ma is the Mach number. Replacing c_s with c/n and Ma with nβ turns the acoustic formula into the Cherenkov formula. Both are instances of the same geometric fact: in a medium supporting waves of finite phase speed, a source exceeding that speed cannot radiate isotropically and must concentrate its emission into a cone.
Cherenkov radiation is the basis of particle detectors that measure particle speed to better than 1% — ring-imaging Cherenkov (RICH) detectors at LHCb and ALICE identify π/K/p by the cone angle. Neutrino telescopes like IceCube and Super-Kamiokande detect Cherenkov light from secondary electrons and muons in a cubic kilometer of ice or water, reconstructing the neutrino direction from the cone. In nuclear reactors, the eerie blue glow of the cooling pool is Cherenkov light from fast electrons Compton-scattered by gamma rays — a direct visual signature of radioactivity. Medical linear accelerators and high-energy physics beamlines all show the same glow.
Drag the speed slider v/c. Keep it below 1/n and no cone forms — you are sub-threshold. Cross the threshold and the blue cone snaps into existence, growing toward its maximum θ_max = arccos(1/n) as v → c. Increase the refractive index n to widen the cone and lower the speed barrier. Try the Reactor Pool preset for the classic water glow, then Sub-threshold to watch the cone vanish, then Mach Cone to see the acoustic analogue with a supersonic source. The Cone Angle plot traces cos θ = 1/(nβ) live; the Spectrum plot shows the 1/λ² bias toward blue.