A pulse of white light is sent straight down a fiber optic cable 1 km long. The refractive index for blue light is 1.639 and for red light 1.621. What time interval will there be between the two components when they reach the far end?
Thus, the blue light is reduced in speed to
and a slowdown of the red light will occur to
In response, the gap in time will be (at least) sixty nanoseconds.
Note: This calculation is valid only if light passes through the cable in a straight line, meaning that there are either no reflections or very few. In reality, though, because of all the reflections, the total pathway will be longer than the kilometer in the question, and there will be more reflections for blue than for red. These two factors will cause the difference to be (much) larger. Therefore, take the answer as a minimal interval.
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The time interval between the blue and red components when they reach the far end is approximately 0.47 nanoseconds.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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