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.

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Section: Chapter Questions

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Concept explainers

Mechanisms of heat transfer

Heat transfer is an essential discipline in thermal engineering that deals with the transfer, conversion, usability, and creation of heat or thermal energy. Transfer of heat occurs through various mechanisms like conduction, convection, radiation, and change of phases. All these mechanisms have distinct characteristics, but these mechanisms can simultaneously occur in an identical system.

Question

•• 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< n,. The numerical aperture of the fiber is defined as sin e,,
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
sin0, = Vn3 – n? assuming the ray is initially in air. Hint: Use of the
Pythagorean theorem may be required.
44
Incident ray
n3-
n2
a
10, 0
2 b
FIGURE 31- 58 Problems 44, 45, and 46
•• ENGINEERING APPLICATION Find the maximum angle of
incidence 0, of a ray that would propagate through an optical fiber
that has a core index of refraction of 1.492, a core radius of
50.00 um, and a cladding index of 1.489. See Problem 44. SSM
45

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