An optical fiber is a flexible, transparent fiber devised to transmit light between the two ends of the fiber. Complete transmission of light is achieved through total internal reflection. This problem aims to calculate the minimum index of refraction n of the optical fiber necessary to obtain total internal reflection for every possible incidence angle.
(a) Express sinθ, where the angle θ is defined in the figure above, in terms of the incidence angle α and the index of refraction n of the optical fiber. Evaluate this function for n=1.5 and α=70∘. Take the index of refraction of air to be 1.
(b) The condition on n for total internal reflection of all beams entering the fiber is achieved when θ=90∘ for all values of α. Determine the smallest value of n that satisfies that condition.