(II) Two rays A and B travel down a cylindrical optical fiber of diameter d = 75

Question

(II) Two rays A and B travel down a cylindrical optical fiber of diameter d = 75.0 mu m, length l = 1.0 km, and index of refraction n1 = 1.465. Ray A travels a straight path down the fiber's axis, whereas ray B propagates down the fiber by repeated reflections at the critical angle each time it impinges on the fiber's boundary. Determine the extra time Delta t it takes for ray B to travel down the entire fiber in comparison with ray A (Fig. 32-58), assuming (a) the fiber is surrounded by air, (b) the fiber is surrounded by a cylindrical glass "cladding" with index of refraction n2 = 1.460.

Explanation / Answer

                   distance move by the light when it is in zigzag pathwhile covering same horizantal distance as the movedtravelled in stright path                d / d' = ns / nm               t / t' = nm / ns               t = nmt'/ns       if we assume that the wire issurrounded by air ns = 1                  sinc =  1 / nm,      where ns is therefractive index of surrounding medium                                                 and nm is the medium in which light is propagating.         from the above relation we can solve for the differencein time of travells in both the paths when moved in strght line and when moved inzig zag path .       distance move by the light when it is in zigzag pathwhile covering same horizantal distance as the movedtravelled in stright path                d / d' = ns / nm               t / t' = nm / ns               t = nmt'/ns       if we assume that the wire issurrounded by air ns = 1                  sinc =  1 / nm,      where ns is therefractive index of surrounding medium                                                 and nm is the medium in which light is propagating.         from the above relation we can solve for the differencein time of travells in both the paths when moved in strght line and when moved inzig zag path .                     t = nmt'/ns       if we assume that the wire issurrounded by air ns = 1                  sinc =  1 / nm,      where ns is therefractive index of surrounding medium                                                 and nm is the medium in which light is propagating.         from the above relation we can solve for the differencein time of travells in both the paths when moved in strght line and when moved inzig zag path .      

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