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

Question

High School

Answer :

akursharma9034 akursharma9034 · Answer 1 · 2024-06-28T19:22:32-04:00

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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