Lag1989 problem number 22.33

Lag1989 problem number 22.33

Express the group velocity U ( ω is the circular frequency; k is the wavenumber) in terms of the phase velocity of light V and dV/dλ and also in terms of V and dn/dλ ( n is the refractive index of the medium; λ is the wavelength in the medium). In what case can the group velocity be greater than the speed of light in vacuum? How to reconcile this with the conclusion of the theory of relativity about the impossibility of signals propagating at a speed greater than that?

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