ENGINEERING APPLICATION An optical fiber allows rays of

Chapter , Problem 44

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ENGINEERING APPLICATION 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 Figure 31-58 the fiber consists of a core material that has an index of refraction and radius b surrounded by a cladding material that has an index of refraction The numerical aperture of the fiber is defined as where is the angle of incidence of a ray of light that impinges on the center of the end of the fiber and then reflects off the corecladding interface just at the critical angle. Using the figure as a guide, show that the numerical aperture is given by assuming the ray is initially in air. Hint: Use of the Pythagorean theorem may be required.