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By observing that red is the outermost color of the rainbow it is possible to conclude the refractive index of water, n, is lower for red than for blue. However, why is n lower for red? This seems to be answered by the Drude dispersion model, with a resonance in the ultraviolet region, but I don't get it because by definition n is related to the speed of light, v, whereas the Drude model discusses the electric susceptibility, χ, as a function of the frequency f, without mentioning the speed of light. In the Drude model n is introduced indirectly by the equation n

^{2}= 1+χ. Should the phase lag of the Drude model, Δφ, be used to explain the variation of v? (Like: v(f) is monotonic increasing because Δφ(f) is monotonic increasing, at the left side of the graph)