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Group Velocity

  1. Aug 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that:

    [tex]\frac{dc}{d\omega}=\frac{1}{k}\left(1-\frac{c}{v_{g}}\right)[/tex]

    3. The attempt at a solution

    [tex]\frac{dc}{d\omega}=\frac{dc}{d\omega}\frac{d\omega}{d\omega}=\frac{dc}{d\omega}\frac{dck}{d\omega}=\frac{dc}{d\omega}k+\frac{dk}{d\omega}c=\frac{dc}{d\omega}k+\frac{c}{v_{g}}=\left\frac{1}{1-k}\right\frac{c}{v_{g}}[/tex]

    ...Yeah, I have no clue. [tex]\omega[/tex], [tex]\lambda[/tex] and c are all functions of each other, and i'm confused :(.
     
    Last edited: Aug 21, 2009
  2. jcsd
  3. Aug 21, 2009 #2
    Nevermind, solved it. I was really close, I just made a stupid mistake with my algebra.
     
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