Page 469 - Engineering Electromagnetics, 8th Edition

CHAPTER 12 Plane Wave Reflection and Dispersion 451

Figure 12.17 See Problems 12.22 and
12.23.
guide. Express, in terms of n 1 and n 2 , the maximum value of φ such that
total confinement will occur, with n 0 = 1. The quantity sin φ is known as
the numerical aperture of the guide.
12.23 Suppose that φ in Figure 12.17 is Brewster’s angle, and that θ 1 is the critical
angle. Find n 0 in terms of n 1 and n 2 .
12.24 A Brewster prism is designed to pass p-polarized light without any
reflective loss. The prism of Figure 12.18 is made of glass (n = 1.45) and is
in air. Considering the light path shown, determine the vertex angle α.
12.25 In the Brewster prism of Figure 12.18, determine for s-polarized light the
fraction of the incident power that is transmitted through the prism, and
from this specify the dB insertion loss, defined as 10log 10 of that number.
12.26 Show how a single block of glass can be used to turn a p-polarized beam of
light through 180 , with the light suffering (in principle) zero reflective loss.
◦
The light is incident from air, and the returning beam (also in air) may be
displaced sideways from the incident beam. Specify all pertinent angles and
use n = 1.45 for glass. More than one design is possible here.
12.27 Using Eq. (79) in Chapter 11 as a starting point, determine the ratio of the
group and phase velocities of an electromagnetic wave in a good conductor.
Assume conductivity does not vary with frequency.
12.28 Over a small wavelength range, the refractive index of a certain material
.
varies approximately linearly with wavelength as n(λ) = n a + n b (λ − λ a ),
where n a , n b and λ a are constants, and where λ is the free-space wavelength.
2
(a) Show that d/dω =−(2πc/ω )d/dλ.(b) Using β(λ) = 2πn/λ,

Figure 12.18 See Problems
12.24 and 12.25.