Components of some computers communicate with each other through optical fibers having an index of refraction n=1.55n = 1.55. What time in nanoseconds is required for a signal to travel 0.200 m through such a fiber?
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Final Answer

1.03 ns1.03 \textrm{ ns}

Solution video

OpenStax College Physics for AP® Courses, Chapter 25, Problem 11 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. We want to know how much time it would take for a light signal to travel 0.200 meters through a material with an index of refraction of 1.55. So, distance is speed times time, and we can solve for time by dividing both sides by V. And so, time is the distance divided by the speed. Now, we need to know what the speed of light is in this material. So, we have index of refraction is the speed of light in the vacuum divided by the speed of light in the material. And, we can solve this for V by multiplying both sides by V over M. And so, we have V equals C over M. So, we can substitute that in for V here. Now, instead of dividing a fraction by a fraction, I'm going to multiply by the reciprocal of V. And so, we have time is distance multiplied by N over C. So, that's 0.200 meters times 1.55 index of refraction divided by the speed of light in the vacuum, giving 1.03 nanoseconds.