1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Computing Cherenkov angle when only knowing n?

  1. May 3, 2015 #1

    1a2

    User Avatar

    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. jcsd
  3. May 3, 2015 #2

    mfb

    User Avatar
    2016 Award

    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.
     
  4. May 3, 2015 #3

    1a2

    User Avatar

    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
     
  5. May 3, 2015 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Hmm... then I guess it asks for the maximal Cherenkov angle.
    At least threshold momentum is clear.
     
  6. May 3, 2015 #5

    1a2

    User Avatar

    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?
     
  7. May 3, 2015 #6

    mfb

    User Avatar
    2016 Award

    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.
     
  8. May 3, 2015 #7

    1a2

    User Avatar

    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
     
  9. May 3, 2015 #8

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    How can you get cos(theta_c)=1/(beta*n)=0? How can 1 divided by something be zero?
     
  10. May 3, 2015 #9

    1a2

    User Avatar

    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
     
  11. May 3, 2015 #10

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    The speed cannot go to infinity, there is a very hard limit to speeds in the universe.
     
  12. May 3, 2015 #11

    1a2

    User Avatar

    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)?
     
  13. May 4, 2015 #12

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Right.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted