Final answer:
The time required for a signal to travel 0.200 meters through an optical fiber with an index of refraction of 1.55 is approximately 1.033 nanoseconds, calculated by dividing the distance by the speed of light in the medium.
Step-by-step explanation:
To determine the time required for a signal to travel 0.200 meters through an optical fiber with an index of refraction of 1.55, we must use the speed of light in the medium, which is given by the formula c/n, where c is the speed of light in a vacuum (approximately 3 x 108 m/s) and n is the index of refraction of the medium.
The speed of light in the fiber is therefore 3 x 108 m/s / 1.55, which equates to approximately 1.935 x 108 m/s. To calculate the time (t) for light to travel the distance (d), we use the formula t = d/v, where v is the speed of light in the fiber. Using the distance of 0.200 meters, the time is thus 0.200 m / 1.935 x 108 m/s, which results in about 1.033 x 10-9 seconds, or 1.033 nanoseconds.
So, the signal would take approximately 1.033 nanoseconds to travel 0.200 meters through an optical fiber with an index of refraction of 1.55.