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One problem with using optical fibers for communication is that light that passes directly down the center of the fiber takes less time to travel from one end to the other than a ray that takes a longer zig-zag path. Light rays that start at the same time but traveling in slightly different directions reach the end of the fiber at different times. This problem can be solved by making the refractive index of the glass gradually change from a higher value in the center to a lower value near the edge. Explain how this reduces the difference in travel times.
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Added Mon, 27 Jul '15
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As the refractive index of the material changes the velocity of light in the medium also changes because

refractive index = (velocity of light in vaccume)/(velocity of light in meedium)= C/V .

====>as the refractive index increases the speed of light in that medium decreases .

Henceby making the refractive index of the glass gradually change from a higher value in the center to

a lower value near the edge this problem can be solved.
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Added Mon, 27 Jul '15
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