I got a relation as follow(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\lambda_k = \frac{2 n(\lambda_k) L}{k}[/tex]

where [tex]\lambda_k[/tex] is a wavelength at mode k, k is integer, n is the index of reflection, L is a constant. I am trying to find the change of wavelength between two adjacent mode approximately, the answer will be

[tex]\Delta\lambda_k \approx \frac{\lambda_k^2}{2n_gL}[/tex]

where

[tex]n_g = n(\lambda_k) - \left.\lambda_k\frac{dn}{d\lambda}\right|_{\lambda_k}[/tex]

I have no idea how to achieve this. Please give me some hint. Thanks

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# How to approximate this relation?

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