Page 467 - Engineering Electromagnetics, 8th Edition

CHAPTER 12 Plane Wave Reflection and Dispersion 449

boundary is (a) reflected; (b) transmitted? (c) What is the standing wave
ratio in region 1?
12.10 In Figure 12.1, let region 2 be free space, while µ r1 = 1, r1 = 0, and is

r1
unknown. Find if (a) the amplitude of E is one-half that of E ;
+
−

1
1
r1
(b) S is one-half of S ;(c) |E 1 | min is one-half of |E 1 | max .
+
−
1
1
12.11 A 150-MHz uniform plane wave is normally incident from air onto a
material whose intrinsic impedance is unknown. Measurements yield a
standing wave ratio of 3 and the appearance of an electric field minimum at
0.3 wavelengths in front of the interface. Determine the impedance of the
unknown material.
12.12 A 50-MHz uniform plane wave is normally incident from air onto the
surface of a calm ocean. For seawater, σ = 4 S/m, and = 78. (a)

r
Determine the fractions of the incident power that are reflected and
transmitted. (b) Qualitatively, how (if at all) will these answers change as
the frequency is increased?
12.13 A right-circularly polarized plane wave is normally incident from air onto a
semi-infinite slab of plexiglas ( = 3.45, = 0). Calculate the fractions

r
r
of the incident power that are reflected and transmitted. Also, describe the
polarizations of the reflected and transmitted waves.
12.14 A left-circularly polarized plane wave is normally incident onto the surface
of a perfect conductor. (a) Construct the superposition of the incident and
reflected waves in phasor form. (b) Determine the real instantaneous form
of the result of part (a). (c) Describe the wave that is formed.
12.15 Sulfur hexafluoride (SF 6 )isa high-density gas that has refractive index,
n s = 1.8ata specified pressure, temperature, and wavelength. Consider the
retro-reflecting prism shown in Fig. 12.16, that is immersed in SF 6 . Light
enters through a quarter-wave antireflective coating and then totally reflects
from the back surfaces of the glass. In principle, the beam should
experience zero loss at the design wavelength (P out = P in ). (a) Determine
the minimum required value of the glass refractive index, n g ,so that the
interior beam will totally reflect. (b) Knowing n g , find the required
refractive index of the quarter-wave film, n f .(c)With the SF 6 gas evacuated

n s n f n g
P in
l/4
P out

Figure 12.16 See
Problem 12.15.