Answer: 1.00
Explanation:
The index of refraction [tex]n[/tex] is a number that describes how fast light propagates through a medium or material.
Being its equation as follows:
[tex]n=\frac{c}{v}[/tex] (1)
Where [tex]c=3(10)^{8}m/s[/tex] is the speed of light in vacuum and [tex]v[/tex] its speed in the other medium and [tex]n=1.55[/tex].
So, from (1) we can find the velocity at which the signal travels and then the time it requires to travel:
[tex]v=\frac{c}{n}[/tex] (2)
[tex]v=\frac{3(10)^{8}m/s}{1.55}[/tex] (3)
[tex]v=193548387.1m/s[/tex] (4)
Now, knowing the velocity [tex]v[/tex] is the distance [tex]d=0.35m[/tex] traveled in a time [tex]t[/tex]:
[tex]v=\frac{d}{t}[/tex] (5)
We can isolate [tex]t[/tex] from (5) and find the value of the required time:
[tex]t=\frac{d}{v}[/tex] (6)
[tex]t=\frac{0.35m}{193548387.1m/s}[/tex] (7)
[tex]t=0.000000001s=1(10)^{-9}s=1ns[/tex] (8) This is the time it takes the signal to travel through the optical fiber: 1 nanosecond.
