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The question asks to determine the most appropriate time to describe how long it takes light to travel across a 10-meter-long optical fiber. Let's work through the problem step-by-step.

### Step 1: Speed of Light in Optical Fiber
The speed of light in a vacuum is approximately \( 3 \times 10^8 \, \text{m/s} \). However, light travels slower in an optical fiber due to the refractive index. Assuming the refractive index \( n \) of the fiber is about 1.5 (a typical value for optical fibers), the speed of light in the fiber would be:

\[
v = \frac{c}{n} = \frac{3 \times 10^8 \, \text{m/s}}{1.5} = 2 \times 10^8 \, \text{m/s}
\]

### Step 2: Calculate Time Taken
Now, use the basic speed equation to calculate the time taken for light to travel the 10-meter distance:

\[
t = \frac{\text{distance}}{\text{speed}} = \frac{10 \, \text{m}}{2 \times 10^8 \, \text{m/s}} = 5 \times 10^{-8} \, \text{seconds}
\]

So, the time it takes for light to travel across the optical fiber is approximately \( 5 \times 10^{-8} \) seconds.

### Step 3: Compare with Options
Let's examine the options provided:

- **(A) \( 3.34 \times 10^{-8} \) second**: This is very close to our calculated time of \( 5 \times 10^{-8} \) seconds and seems like the best approximation.
- **(B) \( 9.28 \times 10^{-12} \) hour**: Converting this to seconds:

\[
9.28 \times 10^{-12} \, \text{hours} \times 3600 \, \text{seconds/hour} = 3.34 \times 10^{-8} \, \text{seconds}
\]

This is also approximately \( 3.34 \times 10^{-8} \) seconds.
- **(C) \( 3.87 \times 10^{-13} \) day**: Converting this to seconds:

\[
3.87 \times 10^{-13} \, \text{days} \times 86400 \, \text{seconds/day} = 3.34 \times 10^{-8} \, \text{seconds}
\]

Again, approximately the same.
- **(D) \( 1.06 \times 10^{-15} \) year**: Converting this to seconds:

\[
1.06 \times 10^{-15} \, \text{years} \times 3.154 \times 10^7 \, \text{seconds/year} = 3.34 \times 10^{-8} \, \text{seconds}
\]

Also close to the same value.

### Conclusion:
All the options are numerically equivalent when converted to seconds. The best answer depends on the preferred time unit. Since the question asks for the most appropriate time, and the fiber length is short, the smallest unit, **seconds**, is the most reasonable choice.

Therefore, the answer is **(A) \( 3.34 \times 10^{-8} \) second**.

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Would you like more details or have any questions about this? Here are some related questions for further practice:

1. How would the time change if the fiber length was doubled?
2. What is the time taken for light to travel 100 meters in vacuum?
3. How does the refractive index of the fiber affect the speed of light?
4. If the speed of light in water is \( 2.25 \times 10^8 \, \text{m/s} \), how long does it take light to travel 5 meters in water?
5. Convert \( 5 \times 10^{-8} \, \text{seconds} \) into microseconds.

**Tip:** When solving physics problems involving light, make sure to account for the medium's refractive index, as it significantly affects the speed of light.

Which of the following is most appropriate to describe the amount of time it takes light to travel across a 10-meter-long optical fiber?

Discover how to calculate the time it takes for light to travel across a 10-meter-long optical fiber using speed, refractive index, and time-distance formulas. Suitable for high school students in grades 9-12.

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