Cherenkov Angle Calculator
Provide the particle speed and the medium’s refractive index to see whether Cherenkov light is emitted.
| Threshold speed c/n | — |
|---|---|
| Emission angle θ | — |
| Status | Enter values to calculate the emission angle. |
The Spark Behind Cherenkov Radiation
Cherenkov radiation occurs when a charged particle travels through a material faster than light can move in that same medium. Although nothing exceeds the speed of light in vacuum , light slows down in a transparent substance. Water, glass, and many plastics have refractive indices greater than one, meaning light’s speed in those materials is . If a particle’s speed exceeds this reduced light speed, it emits a cone of blue light known as Cherenkov radiation.
The Geometric Relation
Imagine a particle moving in a straight line while emitting faint electromagnetic waves. Each tiny pulse spreads outward at the light speed for that medium. Because the particle is moving so quickly, later pulses originate ahead of earlier ones and interfere constructively along a conical surface, forming a bright shock front. The half-angle of this light cone, , depends solely on the particle’s speed and the medium’s refractive index.
Mathematical Formula
Equating the distance light travels in the medium with the distance the particle travels in the same time yields
The angle exists only if exceeds ; otherwise no Cherenkov radiation forms.
Detector Scenarios
Cherenkov detectors rely on the medium’s refractive index to tune the emission cone. The table below highlights common setups.
| Medium | Refractive index | Threshold β | Angle at β = 0.99 |
|---|---|---|---|
| Water | 1.33 | 0.75 | 41.2° |
| Fused silica | 1.46 | 0.68 | 46.8° |
| Heavy gas (C4F10) | 1.0014 | 0.999 | 3.0° |
Threshold β refers to the ratio required to produce light. Lower thresholds make a medium sensitive to slower particles, while gases with indices close to one capture only near-light-speed trajectories.
Cherenkov measurements complement other relativistic diagnostics. For more planning tools, explore the relativistic-kinetic-energy-calculator, synchrotron-critical-frequency-calculator, and relativistic-time-dilation-calculator to model complementary effects in accelerator and astrophysics design.