← Atlas·Cherenkov Cone

Cherenkov Cone

Light travels at c/n in a medium of refractive index n. A charged particle moving faster than that (still < c, no relativity violated) outpaces the light it emits — and a shockwave of photons builds up in a cone behind it. This is why a reactor pool glows blue: electrons moving faster than light-in-water leave a constant cone of optical bow-shock behind them.

particle velocity v

0.85 c

phase velocity c/n

0.75 c

v/(c/n) = β·n

1.13

half-angle θ_c

27.8°

β (v/c) 0.85

n (index) 1.33

wave rate 0.04

cos θ_c = 1 / (β n)

The geometry: in time t, the particle moves v·t; a photon emitted at t=0 has expanded into a sphere of radius (c/n)·t. The cone tangent to all these expanding spheres has half-angle θ_c satisfying cos θ_c = (c/n)/v = 1/(βn). So:

• If βn < 1 (particle slower than light-in-medium), there's no cone — photons spread normally.
• At exactly βn = 1, the cone collapses to a flat plane perpendicular to motion.
• As βn → ∞, the cone closes to a needle pointing forward.

Cherenkov radiation is how IceCube detects neutrinos buried 1 km deep in Antarctic ice: a high-energy neutrino occasionally hits a nucleus, creating a charged lepton (μ or τ) which then radiates a Cherenkov cone of blue photons that PMTs track. The cone's opening angle tells you the lepton's velocity, hence the neutrino's flavor and energy.