Final answer:
Using the index of refraction of 1.55 for the fiber, the speed of light in the fiber is calculated, and then the time for a signal to travel 0.200 meters is found to be approximately 1.0335 nanoseconds.
Step-by-step explanation:
To calculate the time required for a signal to travel through an optical fiber, we need to know the length of the fiber and the speed of light within that fiber. Given the index of refraction (n) of the optical fiber is 1.55, and the length of the fiber is 0.200 meters, we can compute the speed of light in the fiber using the formula v = c/n, where c is the speed of light in a vacuum (approximately 3×108 meters per second).
First, calculate the speed of light in the fiber: v = 3×108 m/s / 1.55, which equals roughly 1.935×108 meters per second. Then, to find the time (t) it takes for light to travel the given distance (d), we use the formula t = d/v.
Time required = 0.200 m / 1.935×108 m/s which equals approximately 1.0335 nanoseconds. Therefore, a signal will take about 1.0335 nanoseconds to travel 0.200 meters through an optical fiber with an index of refraction of 1.55.