In a sample of dense flint glass the phase velocity of light at vacuum wavelength is…

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Optics & Photonics · Wave propagation and light in media

Optics and Photonics, Ch Harmonic waves, phasors and group velocity

Problem

In a sample of dense flint glass the phase velocity of light at vacuum wavelength λ=588 nm\lambda = 588\ \mathrm{nm} is measured to be v=1.947×108 m s−1v = 1.947\times10^{8}\ \mathrm{m\,s^{-1}}, and over a narrow band around that wavelength the phase velocity rises with wavelength at the measured rate dv/dλ=1.00×104 m s−1dv/d\lambda = 1.00\times10^{4}\ \mathrm{m\,s^{-1}} per nm. ((a)) Using vg=v−λ dv/dλv_g = v - \lambda\,dv/d\lambda, find the group velocity at 588 nm, in m s−1\mathrm{m\,s^{-1}}. ((b)) By what percentage does the group velocity fall below the phase velocity?

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