Number of Photons and wavelength?

[vhbelvadi]

I read recently that the "number of photons emitted by a charged particle is inversely proportional to wavelength" with regard to Cerenkov radiations. (The wavelength refers to the radiation which is of comparatively shorter wavelength, towards the blue-end.)

I was looking for a more detailed explanation for this. A little (or a lot of) maths would help too!

Thank you.

 

[jedishrfu]

check out wikipedia for more info on cerenkov radiation:

http://en.wikipedia.org/wiki/Cerenkov_radiation

 

[vhbelvadi]

@jedishrfu - I did that already! Wikipedia states,

"Around the visible spectrum, the relative intensity per unit frequency is approximately proportional to the frequency. That is, higher frequencies (shorter wavelengths) are more intense in Cherenkov radiation."

I was looking for an explanation on how (mathematically) 'relative intensity per unit frequency' and frequency are related. I know they're proportional, but I'd like a mathematical explanation/reasoning for it.

 

[Bill_K]

There's a (rather mathematical) derivation of the Cherenkov frequency spectrum in Jackson.