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?

Question

William Audy · Accepted Answer

The refractive index is also a direct measure of the factor by which the speed of light is slowed down as compared to the speed of light in a vacuum, #c(vac)= 299792458 m / s#  Thus, the blue light is reduced in speed to #c(blue)=299792458/1.639=182911811 m/s# and a slowdown of the red light will occur to #c(red)=299792458/1.621=184942911 m/s# At those speeds the light will reach the end of the cable of 1 km (=1000 m) in a time that can be calculated as
time=distance/speed or #t=s/v# #t(red)=1000/184942911=0.000005407# sec  #->t(red)= 5407# nanoseconds
(nano- meaning one-billionth) #t(blue)=1000/182911811=0.000005467# sec  #->t(blue= 5467# nanoseconds The difference is #5467 -5407=60# nanoseconds  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.

Amelia Adams · Answer

undefined The time interval between the blue and red components when they reach the far end is approximately 0.47 nanoseconds.