The figure shows an optical fiber in which a central plastic core of index of re

Question

The figure shows an optical fiber in which a central plastic core of index of refraction n_1 = 1.64 is surrounded by a plastic sheath of index of refraction n_2 = 1.49. 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 300 m, what is the difference in the travel times along these two routes? Number Units

Explanation / Answer

Consider that the reflected path length is equal to the length of the hypotenuse of a right triangle formed by the centerline ray, the extended reflecting ray, and a line perpendicular to the fiber.

the critical angle:
= sin-1(n2/n1)

= sin-1(1.49 / 1.64)

= 65.304

reflected path length = fiber length / sin(critical angle)
                             = 300 / sin(65.304)

                             = 330.20 m

Path length difference = 330.20 - 300

                                = 30.2 m

We have speed of light , c = 3*10^8 m/s
v = c / 1.64
v = 182926829.3m/s
v = distance / time
time = distance / v
time = (30.2 m) / (182926829.3 m/s)
time = 1.65 x 10^-7 seconds

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