How does the number of photons determine wavelength?

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Discussion Overview

The discussion centers around the relationship between the number of photons and their wavelength, particularly in the context of Cherenkov radiation and the Frank-Tamm formula. Participants explore mathematical and conceptual aspects of this relationship, including derivations and analogies to other spectra.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes that the number of photons at a particular frequency or wavelength is proportional to 1/l², questioning the mathematical basis for this relationship.
  • Another participant suggests that while the number of photons does not depend on wavelength directly, both the wavelength of the photon and the rate of photon production are inter-dependent.
  • A participant seeks clarification on the inter-dependence of wavelength and rate of emission, expressing interest in a derivation of the Frank-Tamm formula.
  • One reply emphasizes the need to derive the Frank-Tamm formula from first principles, suggesting that understanding the process of Cherenkov radiation is essential.
  • An analogy to black-body radiation is introduced, highlighting that the rate of emission and wavelength of photons depend on temperature, allowing for a relationship to be plotted.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the relationship between photon number and wavelength, with no consensus reached on the mathematical derivation or the implications of the Frank-Tamm formula.

Contextual Notes

The discussion includes references to external resources for further reading, but lacks specific mathematical derivations or detailed assumptions underlying the claims made.

vhbelvadi
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While reading on Cerenkov radiations I've been coming across statement to this effect:

It has been noted that the number of photons at a particular frequency or wavelength, as it turns out, is proportional to 1/l2

How is that (mathematically) so?
 
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That's the shape of the spectrum.
http://en.wikipedia.org/wiki/Frank–Tamm_formula

It's not that the number of photons depends on the wavelength it is that the wavelength of the photon and the rate that photons are produced both depend on the same thing.
 
@Simon - So the wavelength of a photon and rate of emission are inter-dependent?

I've been looking for a neat derivation for the Frank-Tamm formula. Any ideas/pages that have it?

And thanks for your reply!
 
Um - not off hand - deriving the F-T formula is what you need to do though.
You should be able to do it from first principles though. Start with how Cherenkov radiation happens in the first place.

It's easy to understand by analogy: look at other common spectra - black-body radiation for eg. I take it you have no problem with the idea that a hot body radiates more in some parts of the EM spectrum than in others? The rate of emmission and the wavelength of the photons both depend on temperature - so we can eliminate the common variable and plot one against the other.
 

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