I know the definition is the ratio of the speed of light in vacuum to the phase velocity of light in the given medium. Here, which color of light do we consider while calculating the ratio? For instance, if we consider the phase velocity of red light, we will get one value for the ratio and if we consider that of violet light, we will get another value.
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Practically for engineering purposes, for transparent materials usually the refractive index data is fitted empirically to a polynomial equation Sellmeire Equation or Cauchy Equation. Often for optical glass, the refractive index and the attenuation coefficient may be given at precisely at at a 632.8 nm since that is a common wavelength, but provide refractive index curves over a wavelength range.
More generally, rather than just considering the refractive index one can think about the dielectric function as a function of wavelength, where the real part of the dielectric function is the square of the refractive index, and the complex part of the dielectric function is related to the absorption.
Mathematically, this allows you to more completely understand the dispersion of the electromagnetic wave since the refractive index and the absorption are related through a Krammers- Kronig relation. This is useful since where there is a strong absorption at a particular wavelength, the refractive index is changing rapidly. The physics is similar to that of a simple harmonic oscillator where the light wave is the driving force and the electron is analogous to a mass bound by a spring to that atoms. In that case the absorption is occurring at a resonance and the refractive index as a function of wavelength is similar in its form as the phase of the oscillator.
