# Homework Help: Computing Cherenkov angle when only knowing n?

1. May 3, 2015

### 1a2

1. The problem statement, all variables and given/known data
If all we know is that the media is 1.001, how can we compute the Cherenkov angle and threshold momentum of electrons,muons, pions, and kaons?

2. Relevant equations
I know that cos(theta_c) = 1/beta*n, where beta = v_p/c and n=c/v_em, where v_p is the particle velocity and v_em is the velocity of the emitted wave.

3. The attempt at a solution
The problem doesn't us what v_p and v_em is. It only tells us the value of n. How are we supposed to find the Cherenkov angle?

2. May 3, 2015

### Staff: Mentor

Can you write down the exact problem statement?

The problem might ask for the maximal cherenkov angle.

You know vem as you know n and c.

3. May 3, 2015

### 1a2

Here is the exact problem statement:

Calculate the Cherenkov angle and the threshold momentum for media with n=1.001, 1.01, 1.03, 1.07, 1.12, 1.33, 1.50 for electrons, muons, pions, kaons, and protons

4. May 3, 2015

### Staff: Mentor

Hmm... then I guess it asks for the maximal Cherenkov angle.
At least threshold momentum is clear.

5. May 3, 2015

### 1a2

so how am I supposed to solve for the Cherenkov angle then, if we can't obtain vp and beta? Should I ask the instructor for a hint or more clarifiation?

6. May 3, 2015

### Staff: Mentor

At which speed do you get the maximal angle?

Asking the instructor for clarification does not harm I guess, but the question above can be answered with the given information.

7. May 3, 2015

### 1a2

the max angle is 90 degrees, right? That occurs when cos(thetac) = 0 ⇒ vem = vp? I don't understand how finding the maximal angle is related to the Cherenkov angle

8. May 3, 2015

### Staff: Mentor

How can you get cos(theta_c)=1/(beta*n)=0? How can 1 divided by something be zero?

9. May 3, 2015

### 1a2

so the max angle occurs when beta→∞. But beta = vp/c, so vp→∞

So we should just set vp→∞ for each of the values for n? The problem asks for the angles, not vp values

10. May 3, 2015

### Staff: Mentor

The speed cannot go to infinity, there is a very hard limit to speeds in the universe.

11. May 3, 2015

### 1a2

so when vp→c? But then that gives beta→1 and thus cos(θc)→1/(1*n)

so for n=1.001, 1.01, 1.03, 1.07, 1.12, 1.33, 1.50, θc = cos-1(1/n)?

12. May 4, 2015

Right.