Problem $2(10$ pts$)$: Light enters the end of a long optical fiber from air as shown below. $[$Take the fiber as extending to the right to infinity.$]$ In order to avoid complications, this optical fiber has no cladding, that is$,$ it is surrounded by air, and we take the fiber as a $2-$dimensional object. The refractive index of air is $n=1\mathrm{.}0,$ and the refractive index of the fiber is $n=1\mathrm{.}2.$

a$)(4$ pts$)$ What range of entering angles $$ between $0-90$ allow the light to enter the end of the fiber? Explain your reasoning.

b$)(6$ pts $)$ What range of entering angles $$ allow the light to be totally internally reflected at subsequent encounters with the walls of the fiber?