Problem 2

A very thick glass sits in air. The glass has a flat surface. A coordinate

system is set up to mark the media with the glass surface to be xy plane. The

air has a dielectric constant €,1 = 1 and the glass €2=4. A plane wave in air

has its electric field described in phasor as

Ē¹ = y 20 e-j(3x+4y)

(V/m)

The field is a traveling wave in air. It is incident on the boundary, indicated

by the super index.

1. Make a sketch to show the media, the boundary, the directions of the field

E¹ and the associated field H¹.

2. Determine the direction of the wave propagation, and the wave front. Add

them to the sketch by drawing a few wave. fronts and the direction of the

direction of the incident wave travels.

77/n3. Find the phase difference in radians per meter between two wave fronts of

this propagating wave in air incident on the glass.

4. Find the time-domain expression of the field E¹ and H¹.

5. Find the impedance of air and that of the glass.

6. Find the angle of incidence, the angle of reflection, and the angle of trans-

mission.

7. Use the impedances and the incident angle to compute the reflection co-

efficient I and the transmission coefficient 7.

8. Find the time-domain expressions of the fields of the reflected wave and

the fields of the transmitted wave. You may use phasors to do the com-

putation. Add to the sketch to indicate the direction of the fields of the

reflected and transmitted waves and the direction they propagate.

9. Determine the time-average power densities of the incident, reflected, and

transmitted waves.