ENGINEERING APPLICATION An optical fiber allows rays 44 of light to propagate long distances by using total internal reflec- tion. 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 n, and radius b sur- rounded by a cladding material that has an index of refraction nz < n,. The numerical aperture of the fiber is defined as sin 0,, where 0, 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 core- cladding interface just at the critical angle. Using the figure as a guide, show that the numerical aperture is given by sine, = Vn3 – n? assuming the ray is initially in air. Hint: Use of the Pythagorean theorem may be required. Incident ray 13. n2 10, 0 FIGURE 31 -58 Problems 44, 45, and 46

ENGINEERING APPLICATION An optical fiber allows rays 44 of light to propagate long distances by using total internal reflec- tion. 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 n, and radius b sur- rounded by a cladding material that has an index of refraction nz < n,. The numerical aperture of the fiber is defined as sin 0,, where 0, 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 core- cladding interface just at the critical angle. Using the figure as a guide, show that the numerical aperture is given by sine, = Vn3 – n? assuming the ray is initially in air. Hint: Use of the Pythagorean theorem may be required. Incident ray 13. n2 10, 0 FIGURE 31 -58 Problems 44, 45, and 46

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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