# How is the k vector related to the index of refraction?

I know k is a vector, bu how does it relate to the index of refraction?

This is for plasma physics, specifically whistler waves

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- gintableLv 710 years agoFavorite Answer
k is called the angular wave number. It is defined such that its magnitude is 2*Pi/lambda, where lambda is wavelength.

Do realize that the formula v=lambda*f must relate frequency to wavelength and wavespeed. Recall index of refraction is defined as n = c/v.

ALSO, most importantly, it is frequency which is unchanged during changing of optically dense media. Wavelength is sacrificial, and thus k is sacrificial as well. Change the value of n, and both lambda and k vary such that v=lambda*f, or v=omega/k can still be satisfied

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