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We have been using group velocity for most purposes as its the velocity with which the wave packet travels, they why do we use phase velocity for calculating refractive index.

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  • $\begingroup$ It falls out that way from maxwells equations, if you have a non dispersive medium. So it is convenient. If you have a medium then it is not precisely true but often close enough for a lot of calculations. If you have some spectral bandwidth or you are more concerned about the pulse shape then it becomes more important to include the dispersive effects. $\endgroup$
    – UVphoton
    May 5 at 21:16

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Group velocity is $\partial \omega /\partial k$ so it involves the derivative of the refractive index to wavenumber/frequency.

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