(adsbygoogle = window.adsbygoogle || []).push({}); 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:)

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# Homework Help: Derive the Sellmeier equation

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