Answer :
It would take approximately 1.03 nanoseconds for the signal to travel 0.200 m through the optical fiber.
To calculate the time required for a signal to travel through an optical fiber, we can use the formula:
t = d / v
Where:
t is the time in seconds,
d is the distance traveled by the signal,
v is the velocity of light in the fiber.
The velocity of light in a medium is given by the formula:
v = c / n
Where:
c is the speed of light in a vacuum,
n is the refractive index of the medium.
The speed of light in a vacuum is approximately [tex]3.00 x 10^8[/tex] meters per second (m/s).
Plugging in the given values:
[tex]v = (3.00 x 10^8 m/s) / 1.55\\v ≈ 1.94 x 10^8 m/s[/tex]
Now we can calculate the time:
[tex]t = (0.200 m) / (1.94 x 10^8 m/s)[/tex]
[tex]t ≈ 1.03 x 10^(-9) seconds[/tex]
Converting to nanoseconds:
t ≈ 1.03 nanoseconds
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