Question

If you want to delay a pulse of light in a laser experiment, you can send the light through a long coil of fiber optic cable. Light travels somewhat slower in the glass core of a fiber than it does in vacuum. We will approximate the speed of light in the fiber as 2.04 x 108 m/s. What length of fiber (in meters) should you use if you want to delay the arrival of light by 121 ns?

Answer 1

To calculate the length of fiber optic cable needed to delay the arrival of light by a certain time, you can use the formula:

\[ \text{Time delay (s)} = \frac{\text{Length of fiber (m)}}{\text{Speed of light in the fiber (m/s)}} \]

First, you need to convert the given time delay of 121 ns into seconds:

\[ \text{Time delay (s)} = 121 \, \text{ns} \times 10^{-9} \, \text{s/ns} = 1.21 \times 10^{-7} \, \text{s} \]

Now, you can rearrange the formula to solve for the length of fiber:

\[ \text{Length of fiber (m)} = \text{Time delay (s)} \times \text{Speed of light in the fiber (m/s)} \]

Plugging in the values:

\[ \text{Length of fiber (m)} = (1.21 \times 10^{-7} \, \text{s}) \times (2.04 \times 10^8 \, \text{m/s}) \]

Calculating the result:

\[ \text{Length of fiber (m)} \approx 24.84 \, \text{meters} \]

So, you should use approximately **24.84 meters** of fiber optic cable to delay the arrival of light by 121 ns.