A $100$ km single mode step$-$index fiber cable with radius of $4mm,n_1=1\mathrm{.}6,n_2=1\mathrm{.}59,$ the fiber cable has a waveguide dispersion of $-10p\frac{s}{km.nm},$ and a material dispersion of $21p\frac{s}{km.nm}.$

Find Dwg

a$)$ The intramodal dispersion.

b$)$ The intermodal dispersion.

c$)$ The length of a compensation shifted fiber with dispersion of $-20ns(km.nm)$ that is required to cancel the total dispersion loss in the fiber.