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Physics / University Physics with Modern Physics (1) 14 / Chapter 33 / Problem 33.46

University Physics with Modern Physics (1) | 14th Edition | ISBN: 9780321973610 | Authors: Hugh D. Young Roger A. Freedman

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Optical fibers are constructed with a cylindrical core

Chapter 33, Problem 33.46

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QUESTION:

Optical fibers are constructed with a cylindrical core surrounded by a sheath of cladding material. Common materials used are pure silica 1n2 = 1.4502 for the cladding and silica doped with germanium 1n1 = 1.4652 for the core. (a) What is the critical angle ucrit for light traveling in the core and reflecting at the interface with the cladding material? (b) The numerical aperture (NA) is defined as the angle of incidence ui at the flat end of the cable for which light is incident on the corecladding interface at angle ucrit (Fig. P33.46). Show that sin ui = 1n 2 1 - n 2 2 . (c) What is the value of ui for n1 = 1.465 and n2 = 1.450?

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QUESTION:

Optical fibers are constructed with a cylindrical core surrounded by a sheath of cladding material. Common materials used are pure silica 1n2 = 1.4502 for the cladding and silica doped with germanium 1n1 = 1.4652 for the core. (a) What is the critical angle ucrit for light traveling in the core and reflecting at the interface with the cladding material? (b) The numerical aperture (NA) is defined as the angle of incidence ui at the flat end of the cable for which light is incident on the corecladding interface at angle ucrit (Fig. P33.46). Show that sin ui = 1n 2 1 - n 2 2 . (c) What is the value of ui for n1 = 1.465 and n2 = 1.450?

ANSWER:

Problem 33.46

Optical fibers are constructed with a cylindrical core surrounded by a sheath of cladding material. Common materials used are pure silica ( = 1,450) for the cladding and silica doped with germanium ( = 1,465) for the core. (a) What is the critical angle for light traveling in the core reflecting at the interface with cladding material? (b) The numerical aperture (NA) is defined as the angle of incidence ?1 at the flat end of the cable for which light is incident on the core-cladding interface at the angle ?crit (Fig.P33.46). Show that (c) What is the value of for = 1,465 and =1,450?

Step by Step Solution

Step 1 of 4

According to Snell’s Law.

Here, is the refractive index of the first medium. is the refractive index of the second medium is the initial angle, and is the refraction angle.

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