•• ENGINEERING APPLICATION An optical fiber allows rays 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 n, < n2. The numerical aperture of the fiber is defined as sin6,, where 6, 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 sin6, = Vn- n assuming the ray is initially in air. Hint: Use of the Pythagorean theorem may be required. 44
•• ENGINEERING APPLICATION An optical fiber allows rays 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 n, < n2. The numerical aperture of the fiber is defined as sin6,, where 6, 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 sin6, = Vn- n assuming the ray is initially in air. Hint: Use of the Pythagorean theorem may be required. 44
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Transcribed Image Text:•• ENGINEERING APPLICATION An optical fiber allows rays
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
n3 < n2. The numerical aperture of the fiber is defined as sine,
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.
44
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