High School

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

Answer :

The time required for a signal to travel 0.200 m through an optical fiber with an index of refraction of n = 1.55 is approximately 1.03 nanoseconds.

To calculate the time required for a signal to travel through the optical fiber, we need to use the formula:

t = d / v

where t is the time, d is the distance traveled by the signal, and v is the velocity of the signal in the medium (which is determined by the index of refraction).

In this case, we are given that the index of refraction is n = 1.55. The velocity of light in a medium with this index of refraction is:
v = c / n
where c is the speed of light in a vacuum (which is approximately 3 x 10^8 m/s).

Plugging in the numbers, we get:
v = (3 x 10^8 m/s) / 1.55 = 1.94 x 10^8 m/s
Now we can calculate the time required for the signal to travel 0.200 m:

t = d / v = (0.200 m) / (1.94 x 10^8 m/s) = 1.03 x 10^-9 s = 1.03 ns

Therefore, the time required for a signal to travel 0.200 m through an optical fiber with an index of refraction of n = 1.55 is approximately 1.03 nanoseconds.

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