Determine the threshold energy for electrons to produce Cerenkov radiation in glass

1. Feb 12, 2012

blueyellow

1. The problem statement, all variables and given/known data

Determine the threshold energy for electrons to produce Cerenkov radiation in glass (refractive index n=1.52).

3. The attempt at a solution

The only equations given in my notes are:

cos $\theta$$_{C}$=1/$\beta$n for $\beta$>1/n

and

dN/d$\lambda$=$\frac{2\pi\alpha}{\lambda^{2}}$L sin$^{2}$ $\theta$$_{C}$

How the second equation relates to the energy, I don't know. What does dN/d$\lambda$ have to do with the energy? And how is the 'threshold' supposed to be worked out?

Is E=mc$^{2}$ in this case? Is the energy supposed to be deduced from $\lambda$?

My textbooks and the internet don't tell me know to do this sort of question either.

2. Feb 12, 2012

diazona

Re: Determine the threshold energy for electrons to produce Cerenkov radiation in gla

What kind of energy exactly is that threshold referring to? Is it the kinetic energy of the electron?

3. Feb 13, 2012

blueyellow

Re: Determine the threshold energy for electrons to produce Cerenkov radiation in gla

The particle needs to travel faster than the local speed of light - the speed of light in the medium - glass, in this case.

So work out the speed of light in glass, and somehow link the speed of light in glass and the speed of the particle in glass. I still don't know what this has to do with the angle or 'N' though.

Thanks if anyone makes it a bit clearer.

4. Feb 15, 2012

diazona

Re: Determine the threshold energy for electrons to produce Cerenkov radiation in gla

Not "somehow" - you said exactly what the link is, that the particle has to be faster than the speed of light in glass. So what is the speed of light in glass? Can you write an inequality expressing the fact that the speed of the particle is greater than the local speed of light?

Can you then think of a way to relate that to the energy?

5. Aug 18, 2012

curiousatlarg

Re: Determine the threshold energy for electrons to produce Cerenkov radiation in gla

The refractive index (n) directly relates to the speed of light in the glass. n = c (speed of light in a vacuum) / v (speed of light in a medium).

6. Aug 18, 2012

curiousatlarg

Re: Determine the threshold energy for electrons to produce Cerenkov radiation in gla

I am rusty at this and my math is slow motion hack work. From what I read, N is the number of electrons intercepting the x axis. The angle is the angle of incidence or the angle of the cone of light emitted. I know it's an old thread, but if you have worked it, I would like to see it. That is my crude interpretation. From what I can see, it is transition radiation. I am just learning the nomenclature and trying to see simple examples at work.