In many transparent materials, dispersion causes different colors (wavelengths)

Question

In many transparent materials, dispersion causes different colors (wavelengths) of light to travel at different speeds. This can cause problems in fiber-optic communications systems where pulses of light must travel very long distances in glass. Assuming a fiber is made of silicate crown glass (see figure below), calculate the difference in travel times that two short pulses of light take to travel 18.8 km in the fiber if the first pulse has a wavelength of 700 nm and the second pulse has a wavelength of 500 nm.

Explanation / Answer

The speed of light in a silicate crown glass is c' = c/n
Where,
c = 3.0 * 10^8 m/s
n is the refractivne index.
n(500) = 1.5125
n(700) = 1.5

c'(500) = (3.0*10^8)/1.5125
c'(700) = (3.0*10^8)/1.50

time = Distance/Velocity
t(500) = (18.8*10^3)/((3.0*10^8)/1.5125)
t(700) = (18.8*10^3)/((3.0*10^8)/1.50)

t = (18.8*10^3)/((3.0*10^8)/1.5125) - (18.8*10^3)/((3.0*10^8)/1.50)
t = 0.78 us

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