An optical fiber allows rays of light to propagate long distances by using total internal reflection. Optical fibers are used extensively in medicine and in digital communications. As shown in the figure below the fiber consists of a core material that has an index of refraction n2 and radius b surrounded by a cladding material that has an index of refraction n3 < n2.
Calculate the difference in time needed for two pulses of light to travel down 13.0 km of the fiber that is described in the figure below. This optical fiber has a core index of refraction of 1.436, a core radius of 50.00 μm, and a cladding index of refraction of 1.433. Assume that one pulse enters the fiber at normal incidence and the second pulse enters the fiber at the maximum angle of incidence. In fiber optics, this effect is known as modal dispersion.