The figure below shows an optical fiber in which a central plastic core of index of refraction n1 = 1.58 is surrounded by a plastic sheath of index of refraction n2 = 1.51. Light can travel along different paths within the central core, leading to different travel times through the fiber. This causes an initially short pulse of light to spread as it travels along the fiber, resulting in information loss. Consider light that travels directly along the central axis of the fiber and light that is repeatedly reflected at the critical angle along the core-sheath interface, reflecting from side to side as it travels down the central core. If the fiber length is 275 m, what is the difference in the travel times along these two routes?
The Attempt at a Solution
This is my initial failed attempt at a solution
The time it takes light traveling at v1 to go 275m:
The time it takes light traveling at v2 to go 275m:
delta t=t1-t2=6.421109383E-8=64.21109383 ns
However, this answer was marked incorrect, so i would like so help figuring out how to solve the problem correctly