Answer :
Final answer:
The time required for a signal to travel 0.35 m through an optical fiber with an index of refraction of 1.55 is calculated to be 1.81 nanoseconds.
Explanation:
The time required for a signal to travel through an optical fiber can be calculated using the equation
δt = d / v,
where δt is the time taken, d is the distance the signal travels, and v is the speed of the signal in the medium. The speed of the signal in the optical fiber (v) is given by c / n, where c is the speed of light in vacuum (3.00 × 108 m/s) and n is the index of refraction of the medium.
Given that the index of refraction (n) is 1.55 for the optical fiber, we first determine the speed of the signal in the fiber and then calculate the required time for a signal to travel 0.35 m.
First, calculate the signal speed in the fiber:
v = c / n
= (3.00 × 108 m/s) / 1.55
= 1.935 × 108 m/s.
Next, calculate the time required for the signal to travel 0.35 m:
δt = d / v
= 0.35 m / (1.935 × 108 m/s)
= 1.81 × 10-9 seconds, or 1.81 nanoseconds.
