In Example 26.10, we discussed how light pulses in a multimode optical fiber are “smeared out” in time due to the different angles of travel that are possible within the fiber. This problem does not occur in single-mode fibers because all light travels along the axis of the fiber, but there is another smearing effect in singlemode fibers due to dispersion. The laser light traveling in the fiber has a small spread in wavelength; hence, a single pulse consists of components of different colors. Since the index of refraction depends on the wavelength, different components of a pulse travel at different speeds, and eventually the faster components of one pulse will “overtake” the slower components of the pulse ahead of it. Consider a light pulse with just two components with wavelengths (in the fiber) of λ₁= 503.0 nm and λ₂ = 504.0 nm, with corresponding indices of refraction n₁ = 1.5500 and n₂ = 1.5510, traveling in a fiber of length 20 km.

(a) Which wavelength travels fastest?

(b) How long will it take each component to travel the entire length of the fiber? 

(c) Two very short pulses, one with wavelength λ₁ and another with λ₂, are started simultaneously at one end of the fiber. When the faster component reaches the end of the fiber, how far behind is the slower component?