Past exam of the physics A course of the University of Cambridge / 2017 / Paper 2 / Section B / B7 / Which wavelength enters the derivative formula

For the wavelength in the medium, ${\lambda }_m=2\pi /k$, differentiate $\omega =k{v}_p(k)$:The distinction in group velocity in material and vacuum wavelength coordinates is essential for the numerical data. For incident vacuum wavelength ${\lambda }_0=2\pi c/\omega$, differentiation of $k=\omega /v_p({\lambda }_0)$ instead givesThus the printed derivative identity is valid, but its wavelength coordinate cannot be carried unchanged into data specified before refraction.