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Derive the Sellmeier equation

  1. Aug 28, 2011 #1
    1. The problem statement, all variables and given/known data
    Derive the Sellmeier equation
    [itex]n^{2} = 1 + \frac{A\lambda^{2}_{vac}}{\lambda^{2}_{vac}-\lambda^{2}_{0,vac}}[/itex]
    [itex](n+i\kappa)^{2}= 1 + \frac{\omega^{2}_{p}}{\omega^{2}_{0}-
    i\omega\gamma - \omega^{2}}[/itex]

    for a gas or glass with negligible absorption (i.e. [itex]\gamma[/itex] ≈ 0, valid far
    from resonance [itex]\omega_{0}[/itex], where [itex]\lambda_{0,vac}[/itex]
    corresponds to frequency [itex]\omega_{0}[/itex] and A is a constant.

    2. Relevant equations
    [itex]\omega = \frac{2\pi c}{\lambda_{vac}}[/itex]

    [itex]\omega^{2}_{p}= \frac{Nq^{2}_{e}}{\epsilon_{0}m_{e}}[/itex]

    3. The attempt at a solution

    Since the absorption is negligible, [itex]\gamma = 0[/itex] we can drop the imaginary part , and I will substitute directly for [itex]\omega[/itex] and [itex]\omega_{p}[/itex] from the above equations. It gives this result:

    [itex]1+ \frac{\lambda^{2}_{vac}\lambda^{2}_{0,vac}\frac{Nq^{2}_{e}}{4\pi^{2}c^{2}\epsilon_{0}m_{e}}}{\lambda^{2}_{vac}-\lambda^{2}_{0,vac}}[/itex]

    i.e. everything is ok expect that i have on extra of [itex]\lambda^{2}_{0,vac}[/itex] in the numerator. What have I done wrong? Very thankful for all help:)
  2. jcsd
  3. Dec 6, 2014 #2
    I know the thread is 3 years old but any idea on this question? Have a similiar problem, appreciate any help
  4. Dec 6, 2014 #3


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    Homework Helper

    Nothing is wrong. That "extra" [itex]\lambda^{2}_{0,vac}[/itex] is included into the constant A.
  5. Dec 6, 2014 #4
    That's what I was thinking but wasn't sure since that term appeared elsewhere in the formula, thanks for your help!
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