Over a small wavelength range, the refractive index of a certain material varies approximately linearly with wavelength as n(λ) = n_a + n_b(λ − λ_a), where n_a, n_b and λa are constants, and where λ is the free-space wavelength.

(a) Show that d/dω = −(2πc/ω²)d/dλ.

(b) Using β(λ) = 2πn/λ, determine the wavelength-dependent (or independent) group delay over a unit distance.

(c) Determine β₂ from your result of part (b).

(d) Discuss the implications of these results, if any, on pulse broadening.