It is explained that Cherenkov radiation is light that emit a particle inside a refractive material when the speed of the emitted light is slower than $c$. So my hypothetical question is what would be the frequency of that light or radiation if the speed of the particle and the speed of the radiation were equal?
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Cherenkov light is emitted when the particle moves in a medium with a speed higher than the speed of light in that medium. This radiation does not have a single frequency, the spectrum is wide and higher frequencies have higher intensity.
When the particle has the same speed as speed of light in the medium at some frequency ($c/n(\omega)$), no energy is put into radiation at that frequency. This follows from the Frank-Tamm formula describing radiation intensity as function of frequency and speed of the particle. The moving particle has to be faster than speed of light at that frequency, to emit Cherenkov radiation at that frequency.
answered Jul 9, 2023 at 11:16