Chapter 12, Problem 12.28P

Over a small wavelength range, the refractive index of a certain material vanes approximately linearly with wavelength as n( $\lambda$ ) = na + nb( $\lambda$ - $\lambda$ ), where n_a, n_b and $\lambda$ are constants, and where >. is the free-space wavelength.

(a) Show that $d/d\omega =-\left(2\pi c/{\omega }^2\right)d/d\lambda .$

(b) Using $\beta \left(\lambda \right)=2\pi x/\lambda ,$ determine the wavelength-dependent (or independent) group delay over a unit distance (c) Determine 3; horn your results of part b, (a) Discussion the implications of these results, if any, on pulse broadening