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Relation between group velocity and phase velocity

  1. Apr 17, 2013 #1
    1. The problem statement, all variables and given/known data

    k2mnp1.png


    2. Relevant equations



    3. The attempt at a solution
    2hg8yt1.png

    Is my initial assumption wrong?
     
  2. jcsd
  3. Apr 17, 2013 #2

    rude man

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    No, it's right.
     
  4. Apr 18, 2013 #3
    But I seem to be missing out on a 1/vph term..
     
  5. Apr 18, 2013 #4

    rude man

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    You asked if you initial assumption was right. I did not check all your work. Will try later.
     
  6. Apr 18, 2013 #5

    rude man

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    You wrote dk/dw = (2pi/0)dn/dw.

    However, k depends on more than w:
    dk = ∂k/∂w dw + ∂k/∂n dn

    So 1/vg = dk/dw = ∂k/∂w + ∂k/∂n dn/dw
    = n/c + (w/c) dn/dw
    Etc.
     
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