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Homework Help: Phase velocity in glass

  1. Apr 15, 2015 #1
    1. The problem statement, all variables and given/known data
    a) Starting from Equation 5-1, show that the group velocity can also be expressed as: vg = vp - λ(dvp/dλ)

    b) The phase velocity of each wavelength of white light moving through ordinary glass is a function of the wavelength; that is, glass is a dispersive medium. What is the general dependence of vp on λ in glass? Is dvp/dλ positive or negative?

    I'm mostly concerned about part b, but I have a question about part a as well.

    2. Relevant equations
    Equation 5-1: f = E/h
    vp = ω/k = fλ
    vg = vp + k(dvp/dk)
    n = c/v

    3. The attempt at a solution

    a) Using the last two equations I listed and just plugging in what k equals as well as what dk equals after differentiating the second equation in terms of wavelength, it is very easy to see how to get the the equation they want from the equation we were given in class. What I don't understand is how Eq. 5-1 comes into it, and what they want you to show "starting from" that equation. Any ideas?

    b) I feel like this is simple but I'm not sure how to start because I am confusing all the different velocities and terms. Once I have vp(λ) I'll differentiate it to easily answer the second part. Any hints on how to begin to find vp(λ)? Is the v in n = c/v equal to vp, or is it equal to the actual velocity of the particle which is 2vp?
  2. jcsd
  3. Apr 16, 2015 #2

    This is what I came up with for b:

    vp = c/n
    c = fλ

    vp = fλ/n

    dvp/dλ = f/n = positive

    I have no idea if this is right. Seems too simple.
    Last edited: Apr 16, 2015
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