Cherenkov Radiation Cone

What you are seeing: a charged particle traversing a transparent medium of refractive index $n$ at speed $\beta c$ . Each point on its track emits a spherical light wavelet that expands at $c/n$ ; when $\beta n > 1$ those wavelets pile up on a cone of half-angle $\cos\theta_C = 1/(\beta n)$

Figure 1. Cherenkov wavelets from a charged particle moving through a medium with refractive index n; the cone envelope appears once beta*n exceeds 1. Method: closed-form geometry of spherical wavelets emitted along the particle track.

β = v/c0.85

medium1.33

animation speed2

wavelets shown24

WHAT TO TRY

Raise beta above 1/n for the medium: the particle outruns its own light and a shock cone forms, just as a supersonic jet makes a Mach cone. Below that threshold there is no Cherenkov light.
Switch the medium (water, silica, lead glass): a higher refractive index lowers the threshold speed and widens the cone, since cos(theta_C) = 1/(n beta).
Watch the spherical wavelets stack: each point on the track emits a sphere, and they pile up into the coherent cone, the blue glow of a reactor core.