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Home/Electricity & Magnetism/Cherenkov Radiation Cone

Cherenkov Radiation Cone

This interactive simulator explores Cherenkov Radiation Cone in Electricity & Magnetism. 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. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: For learners comfortable with heavier math or second-level detail. Typical context: Electricity & Magnetism.

Key terms

  • cherenkov
  • radiation
  • cone
  • cherenkov cone
  • electricity
  • magnetism

Particle & medium

0.85
1.333

When a charged particle exceeds the phase velocity of light c/n in a medium, its wavefronts pile up on a Mach-like cone with half-angle satisfying cos θ_c = 1/(βn). Below the threshold β_thr = 1/n no cone forms. The classic blue glow of pool-type research reactors and the directional pulses recorded by IceCube and Super-Kamiokande are direct consequences. The simulation renders spherical wavefronts in the medium (cyan), the relativistic particle (yellow) and the resulting Cherenkov cone (magenta).

Measured values

n1.3330
β threshold0.7502
cos θ_c0.8826
θ_c28.05°

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.