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(a) Show that the group velocity and phase velocity are

related by:

v_group = v_phase - λv_phase/dλ

(b) When white light travels through glass, the phase velocity

of each wavelength depends on the wavelength. (This is

the origin of dispersion and the breaking up of white light

into its component colors—different wavelengths travel at

different speeds and have different indices of refraction.)

How does vphase depend on λ? Is dvphase/dλ positive or

negative? Therefore, is vgroup >vphase or < vphase?

Edit
Added Thu, 11 Feb '16
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Solutions
-1

V_phase = w/k

k = 2*pi / λ

dk = -2*pi/ λ^2

dw/dk = d(V_phase)/dk * k + dk/dk + V_phase

Edit
Added Thu, 11 Feb '16
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