Page 468 - Engineering Electromagnetics, 8th Edition

450 ENGINEERING ELECTROMAGNETICS

from the chamber, and with the glass and film values as previously found,
find the ratio, P out /P in . Assume very slight misalignment, so that the long
beam path through the prism is not retraced by reflected waves.
12.16 In Figure 12.5, let regions 2 and 3 both be of quarter-wave thickness.
Region 4 is glass, having refractive index, n 4 = 1.45; region 1 is air. (a)
Find η in,b .(b) Find η in,a .(c) Specify a relation between the four intrinsic
impedances that will enable total transmission of waves incident from the
left into region 4. (d) Specify refractive index values for regions 2 and 3 that
will accomplish the condition of part (c). (e) Find the fraction of incident
power transmitted if the two layers were of half-wave thickness instead of
quarter wave.
12.17 A uniform plane wave in free space is normally incident onto a dense
dielectric plate of thickness λ/4, having refractive index n. Find the
required value of n such that exactly half the incident power is reflected
(and half transmitted). Remember that n > 1.
12.18 A uniform plane wave is normally incident onto a slab of glass (n = 1.45)
whose back surface is in contact with a perfect conductor. Determine the
reflective phase shift at the front surface of the glass if the glass thickness is
(a) λ/2; (b) λ/4; (c) λ/8.
12.19 You are given four slabs of lossless dielectric, all with the same intrinsic
impedance, η, known to be different from that of free space. The thickness
of each slab is λ/4, where λ is the wavelength as measured in the slab
material. The slabs are to be positioned parallel to one another, and the
combination lies in the path of a uniform plane wave, normally incident.
The slabs are to be arranged such that the airspaces between them are either
zero, one-quarter wavelength, or one-half wavelength in thickness. Specify
an arrangement of slabs and airspaces such that (a) the wave is totally
transmitted through the stack, and (b) the stack presents the highest
reflectivity to the incident wave. Several answers may exist.
12.20 The 50-MHz plane wave of Problem 12.12 is incident onto the ocean
surface at an angle to the normal of 60 . Determine the fractions of the
◦
incident power that are reflected and transmitted for (a) s-polarization, and
(b) p-polarization.
12.21 A right-circularly polarized plane wave in air is incident at Brewster’s angle
onto a semi-infinite slab of plexiglas ( = 3.45, = 0). (a) Determine the

r
r
fractions of the incident power that are reflected and transmitted.
(b) Describe the polarizations of the reflected and transmitted waves.
12.22 A dielectric waveguide is shown in Figure 12.17 with refractive indices as
labeled. Incident light enters the guide at angle φ from the front surface
normal as shown. Once inside, the light totally reflects at the upper n 1 − n 2
interface, where n 1 > n 2 . All subsequent reflections from the upper and
lower boundaries will be total as well, and so the light is confined to the