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!

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]
    from
    [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

    ehild

    User Avatar
    Homework Helper
    Gold Member

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

Have something to add?
Draft saved Draft deleted



Similar Discussions: Derive the Sellmeier equation
  1. Deriving an equation (Replies: 1)

  2. Deriving an equation? (Replies: 3)

  3. Derive the equation (Replies: 13)

  4. Derive an equation (Replies: 3)

Loading...