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Neutrinos · D09 · Water and geometry

Cherenkov Light & Detector Rings

When does a cone of light become a ring? When it hits a surface lined with light sensors. The particle's speed sets the opening angle of the cone. Its direction and its distance from that surface then decide where the light lands, and so the shape and size of the ring you record.

Set a charged particle’s speed and tilt, then follow its light to a flat square detector. Move the emission point to see which parts of the pattern come from the cone’s geometry and which come from the detector’s finite size.

Interactive modelCherenkov Light & Detector Rings
Cherenkov half-angle—\text{—}
Speed threshold · fraction of vacuum light speed—\text{—}
Recorded rays—\text{—}
Outside the finite plane—\text{—}
Normal-incidence reference radius—\text{—}
Mean recorded optical path—\text{—}

Recorded data from a teaching simulation

Inspect the measurement

Preparing a reproducible teaching record…

Read a sample of the record
Scientific reference ↗Read the worldwide history →2026 Nobel Prize in Physics →

Physics tutorial

A cone meets a measurement plane

BackgroundThe detector plane faces along positive z; x is horizontal and y is vertical, all in metres. The charged particle moves in the plane spanned by x and z. Its small emission region sits at z equal to zero, shifted sideways by the chosen offset.

Why it mattersWhat changes the cone of light itself, and what only changes the pattern it leaves on the detector?

Start with the essentials

Focus question
What changes the cone of light itself, and what only changes the pattern it leaves on the detector?
One-sentence intuition
The particle’s speed sets the Cherenkov angle; the track’s tilt and the distance to the detector set the shape you record.

Core mathematical model

Cherenkov angle and speed threshold

cos⁡θC=1nβ,nβ>1\cos\theta_C=\frac{1}{n\beta},\qquad n\beta>1

The speed ratio here is the particle’s speed divided by the speed of light in vacuum. Below the threshold this model emits no light. The refractive index is taken to be the same at every wavelength.

Where each ray meets the plane, and the radius at normal incidence

rD=r0+zDkzk,Rα=0=zDtan⁡θC\mathbf r_D=\mathbf r_0+\frac{z_D}{k_z}\mathbf k,\qquad R_{\alpha=0}=z_D\tan\theta_C

The ray’s unit direction is k. Only rays that travel forward and land inside the square are recorded. The radius for a track perpendicular to the plane stays on screen as a reference even when the track is tilted; it is not fitted to the ring.

Common difficulties

A cone meets a measurement plane

Typical misconceptionThe ring is a picture of the neutrino itself.

Better mental modelThe ring is light from a charged particle that the neutrino produced. Working back to the neutrino also takes the kinematics of the interaction and the detector response.

Run the experiment

  1. 01

    Cross the threshold

    Choose Below threshold. Raise the speed until light appears.

    What to observe: The cone opens from zero angle. Above threshold the model always samples the same number of rays, so the brightness tells you nothing about how much light a real particle gives off.
  2. 02

    Tilt the cone

    Choose Tilted cone and compare the apparatus with the recorded plane.

    What to observe: A tilted cone leaves a shifted, stretched pattern, and the edge of the square can cut part of it off.
  3. 03

    Change distance only

    Return to Centered ring and double the emission-to-plane distance.

    What to observe: The ring’s radius doubles while the cone angle stays the same, until the ring runs past the edge of the square.

Related experiments and articles

Continue exploring

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