Question

Components of some computers communicate with each other through optical fibers having an index of refraction n =1.55. What time in nanoseconds is required for a signal to travel 0.35 m through such a fiber? Your answer should be a number with two decimal places, do not include the unit.

Answer 1

Answer: 1.00

Step-by-step explanation:

The index of refraction
`n` is a number that describes how fast light propagates through a medium or material.

Being its equation as follows:

`n=(c)/(v)` (1)

Where
`c=3(10)^(8)m/s` is the speed of light in vacuum and
`v` its speed in the other medium and
`n=1.55`.

So, from (1) we can find the velocity at which the signal travels and then the time it requires to travel:

`v=(c)/(n)` (2)

`v=(3(10)^(8)m/s)/(1.55)` (3)

`v=193548387.1m/s` (4)

Now, knowing the velocity
`v` is the distance
`d=0.35m` traveled in a time
`t`:

`v=(d)/(t)` (5)

We can isolate
`t` from (5) and find the value of the required time:

`t=(d)/(v)` (6)

`t=(0.35m)/(193548387.1m/s)` (7)

`t=0.000000001s=1(10)^(-9)s=1ns` (8) This is the time it takes the signal to travel through the optical fiber: 1 nanosecond.