Final answer:
To calculate the time required for a signal to travel 0.200 m in an optical fiber with an index of refraction of 1.55, one must use the formula t = d / (c/n), resulting in approximately 1.03 nanoseconds.
Step-by-step explanation:
To determine the time required for a signal to travel through a fiber-optic cable with an index of refraction n = 1.55, we use the relationship between the speed of light in a vacuum (c), the index of refraction, and the distance d the light needs to travel. The speed of light in the fiber is given by v = c/n, where c is the speed of light in vacuum (approximately 3 x 10^8 m/s).
To find the time t, we can rearrange the equation v = d/t, giving us t = d/v. Plugging in the distance d = 0.200 m and the speed of light in the fiber v = c/n, we calculate the time it takes for the signal to travel the given distance.
- Calculate the speed of light in the fiber: v = c/n = (3 x 10^8 m/s) / 1.55 ≈ 1.935 x 10^8 m/s
- Calculate the time of travel: t = d/v = 0.200 m / (1.935 x 10^8 m/s)
Performing the calculation yields:
t ≈ 1.03 nanoseconds.
Therefore, it takes approximately 1.03 nanoseconds for a signal to travel 0.200 meters through an optical fiber with an index of refraction of 1.55.