Charged particle in a medium of refractive index n: spherical wavefronts of phase velocity c/n pile up on a Mach-like cone with half-angle cos θ_c = 1/(βn) once β > 1/n. Animated wavefronts, magenta cone envelope and material presets (water, glass, diamond) explain the blue glow of pool reactors and IceCube/Super-Kamiokande detection.
About this model
A charged particle moving through a dielectric of refractive index n emits electromagnetic radiation when its speed v = βc exceeds the phase speed of light in the medium, c/n. Spherical wavefronts pile up on a Mach-like cone whose half-angle satisfies cos θ_c = 1/(βn). The lab animates those wavefronts, a magenta cone envelope, and material presets (water, glass, diamond) so you can see how n and β set the opening angle. Assumptions: uniform isotropic medium, constant particle velocity, and geometric optics of the wavefront envelope—no full spectral intensity or polarization. Vary β and the medium to watch the cone appear only for β > 1/n and open wider as βn increases.
Who it's for: Advanced undergraduate and graduate particle physics, nuclear physics, and radiation-detection courses.
Key terms
Cherenkov radiation
Cherenkov angle
refractive index
phase velocity
β threshold
particle detector
How it works
Cherenkov radiation simulator: a charged particle of speed v = βc traversing a medium of refractive index n. Spherical light wavefronts of speed c/n form a Mach-like cone with half-angle cos θ_c = 1/(βn) when β > 1/n. Below threshold the wavefronts overtake the particle; above threshold the magenta cone is the famous Cherenkov radiation pattern.
Frequently asked questions
Why is there a speed threshold?
Light in the medium travels at c/n, not c. If the particle is slower than that phase speed, wavefronts never catch up into a coherent cone. The condition β > 1/n is geometric, not a quantum barrier—below threshold there is still polarization response, but no Cherenkov cone.
Does a larger θ_c mean a faster particle?
From cos θ_c = 1/(βn), larger β (or larger n) makes θ_c larger—the cone opens wider toward 90°. A common mix-up with sonic booms is thinking the angle shrinks with speed; here faster particles open the cone until β→1.
Why do pool reactors and IceCube look blue?
Cherenkov spectra favor shorter wavelengths in the visible, so water detectors glow blue. IceCube and Super-Kamiokande use that light timing and pattern—this simulator shows the cone geometry that underlies those rings, not the full photon yield.