What Is Cherenkov Radiation? The Blue Wake of Fast Particles

Cherenkov radiation is the faint blue light given off when an electrically charged particle moves through a transparent material, such as water or ice, faster than light itself can travel through that material. Our character Azurwake, on the Azurwake sticker, personifies it, with a cone of blue light trailing behind like the wake of a boat. This post builds on our explainer Why Is the Speed of Light the Limit?, because the first question everyone asks is how this is possible when nothing can beat the speed of light in a vacuum.

Who discovered Cherenkov radiation?

In 1934, while working under Sergei Vavilov in Moscow, Pavel Cherenkov saw blue light coming from a bottle of water that was being hit by radiation (NobelPrize.org, Cherenkov biography^[1]). He published a careful study in English in 1937, under the title “Visible Radiation Produced by Electrons Moving in a Medium with Velocities Exceeding that of Light” (Čerenkov, 1937^[2]). The explanation came from Ilya Frank and Igor Tamm in 1937, and the three shared the 1958 Nobel Prize in Physics “for the discovery and the interpretation of the Cherenkov effect” (NobelPrize.org, Physics 1958^[3]).

How can a particle outpace light in water?

Nothing outruns light in a vacuum, where its speed is exactly c = 299 792 458 m/s (NIST, speed of light^[4]). In a material, light is slower. The refractive index n tells you by how much: light travels at v = c/n. For fresh water n = 1.333, and for ice n = 1.309 (OpenStax College Physics 2e, §25.3^[5]). So light in water moves at about 299 792 458 / 1.333 ≈ 2.25 × 10⁸ m/s, roughly 75% of its vacuum speed.

A fast electron or muon is slowed far less by the water than the light is. If its speed is above c/n, it really is overtaking the light in that medium, and relativity is not broken, because the particle is still slower than c. The 1958 presentation speech made the comparison everyone uses: a boat moving faster than the waves on the water makes a bow wave, and a jet faster than sound makes a sonic bang. Cherenkov light is the optical version of that wake (NobelPrize.org, 1958 ceremony speech^[6]).

The Cherenkov angle formula

The light leaves on the surface of a cone around the particle’s path. The Particle Data Group gives the angle θ between the light and the particle’s direction (Groom & Klein, PDG 2024, §34.7^[7]):

cos θ = 1 / (nβ)

Here β = v/c is the particle’s speed as a fraction of the speed of light (no units), n is the refractive index (no units), and θ is in degrees or radians. Because cos θ cannot be larger than 1, light is only emitted when nβ is greater than 1. That gives the threshold, which the same review states as β_t = 1/n:

β > 1 / n

Worked example: electrons in water

For water, 1/n = 1/1.333 = 0.750, so a particle must move faster than 75.0% of c. For a particle at almost c (β ≈ 1), cos θ = 1/1.333, so the cone opens to its widest angle, θ ≈ 41.4°.

How much energy does an electron need? At the threshold the Lorentz factor is γ = 1/√(1 − β²) = 1/√(1 − 0.5628) ≈ 1.512. The electron’s rest energy is 0.511 MeV (PDG 2024, lepton summary table^[8]), so its kinetic energy must exceed (γ − 1) × 0.511 MeV ≈ 0.26 MeV. Electrons from many radioactive decays carry more than that, which is why a swimming-pool reactor glows. As the 1958 speech put it, the whole core is aglow with blue Cherenkov light (NobelPrize.org, 1958 ceremony speech^[6]). For ice, the same steps give β > 0.764 and a widest angle of about 40.2°.

Why is Cherenkov light blue?

The number of photons emitted per centimetre of path depends on wavelength λ as 1/λ²: the PDG formula is d²N/dx dλ = (2παz²/λ²)(1 − 1/(β²n²)), where α ≈ 1/137 is the fine-structure constant and z is the particle’s charge number (Groom & Klein, PDG 2024^[7]). Shorter wavelengths win, so the light is weighted toward the blue and ultraviolet end of the spectrum. The PDG also gives a handy count: about 370 sin²θ photons per eV of photon energy per centimetre of track for a singly charged particle. In water at β ≈ 1, sin²θ = 1 − 1/1.333² ≈ 0.437, so that is roughly 160 photons per eV per cm. The light is faint, which is why detectors need sensitive photomultiplier tubes.

Cherenkov light is not the same as the glow of a hot object, and not fluorescence. It comes from the moving charge disturbing the material around it, and it stops the moment the particle drops below the threshold speed.

How physicists use the blue glow

Counting particles and measuring their speed

Because light appears only above a set speed, and its angle tells you the speed, a Cherenkov detector can pick out fast particles and measure them. The 1958 speech notes that a detector of this kind played a decisive part in the 1955 discovery of the antiproton (NobelPrize.org, 1958 ceremony speech^[6]).

IceCube: a cubic kilometre of Antarctic ice

The IceCube Neutrino Observatory at the South Pole uses natural ice as its detector material. Its in-ice part has 5,160 digital optical modules, each with a ten-inch photomultiplier tube, on 86 vertical strings frozen into the ice between 1,450 m and 2,450 m deep (IceCube, “IceCube Detector”^[9]). Neutrinos almost never interact, but when one does, it can produce a charged particle that moves faster than light travels in ice. The modules record its Cherenkov light, and the pattern of hits gives its direction and energy.

Where to go next

You will find Azurwake and more of our characters in our physics stickers collection, and more particle designs in our Particle & Nuclear Physics collection. For the decays that produce many of these fast electrons, read Beta Decay Unveiled.

Quick FAQ

Does Cherenkov radiation break relativity?

No. The particle is faster than light in the material, c/n, but always slower than c, the speed of light in a vacuum.

Does it happen in air?

Yes, but the refractive index of air is very close to 1, so the threshold speed is very close to c and the cone angle is small.

Is the blue glow dangerous to look at?

The light itself is ordinary visible light. The danger is the radiation that produces it, which is why reactor pools are shielded by metres of water.

References

1. NobelPrize.org, “Pavel A. Cherenkov – Biographical”. https://www.nobelprize.org/prizes/physics/1958/cerenkov/biographical/
2. P. A. Čerenkov (1937), “Visible Radiation Produced by Electrons Moving in a Medium with Velocities Exceeding that of Light,” Phys. Rev. 52, 378–379 (DOI 10.1103/PhysRev.52.378; metadata verified via Crossref). https://doi.org/10.1103/PhysRev.52.378
3. NobelPrize.org, “The Nobel Prize in Physics 1958” (P. A. Cherenkov, I. M. Frank & I. E. Tamm). https://www.nobelprize.org/prizes/physics/1958/summary/
4. NIST CODATA 2022 recommended values: speed of light in vacuum (exact). https://physics.nist.gov/cgi-bin/cuu/Value?c
5. P. P. Urone & R. Hinrichs, College Physics 2e (OpenStax, Rice University), §25.3 “The Law of Refraction”. https://openstax.org/books/college-physics-2e/pages/25-3-the-law-of-refraction
6. NobelPrize.org, Award ceremony speech, Nobel Prize in Physics 1958. https://www.nobelprize.org/prizes/physics/1958/ceremony-speech/
7. D. E. Groom & S. R. Klein, “Passage of Particles Through Matter,” in S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024), §34.7 Cherenkov radiation. https://pdg.lbl.gov/2024/reviews/rpp2024-rev-passage-particles-matter.pdf
8. S. Navas et al. (Particle Data Group) (2024), Review of Particle Physics: Leptons summary table. https://pdg.lbl.gov/2024/tables/rpp2024-sum-leptons.pdf
9. IceCube Neutrino Observatory (University of Wisconsin–Madison), “IceCube Detector”. https://icecube.wisc.edu/science/icecube/

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.