Suez Canal University (SCU)
Department of Electronics and Electrical Engineering
Sheet 3: Microwave Engineering (Part 2)
Dr.-Ing. Doaa Ahmed
Answer the following questions
1. A plane wave in air is incident on a soil surface at an angle of incidence θi = 50◦ . The relative
permittivity of air is r1 = 1, and the relative permittivity of the soil is r2 = 4.
Calculate the reflection and transmission coefficients for perpendicular polarization (TE) and
parallel polarization (TM). Additionally, determine the Brewster angle.
2. A plane wave radiated by a distant antenna is incident upon a plane soil surface located at
z = 0. The electric field of the incident wave is given by:
~ i = ŷ100 cos(ωt − πx − 1.73πz) (V/m).
E
The soil medium is a lossless dielectric with a relative permittivity r = 4.
1. Determine the wave number in air k1 , the wave number in soil k2 , and the angle of incidence
θi .
2. Obtain expressions for the total electric fields in air and in the soil.
3. Determine the average power density carried by the wave traveling in soil.
3. A 5 W beam of light is incident in air upon the plane boundary of a dielectric medium with
an index of refraction of 5. The angle of incidence is θi = 60◦ , and the incident wave is parallel
polarized (TM). Determine the transmission angle and the powers contained in the reflected
and transmitted beams.
4. Light is incident from air to glass at Brewsters angle. Determine the incident and transmitted
angles.
5. Express the normal-incidence reflection coefficient at the boundary between two nonmagnetic,
conducting media in terms of their complex permittivities.
6. Determine the average power densities in media 1 and 2 for the fields described by:
~ 1 (z) = x̂E0i (e−γ1 z + Γeγ1 z ),
E
i
~ 1 (z) = ŷ E0 (e−γ1 z − Γeγ1 z ),
H
ηc1
assuming medium 1 is slightly lossy with ηc1 approximately real.
where:
- γ1 = α1 + jβ1 , the complex propagation constant in medium 1.
- ηc1 , the characteristic impedance of medium 1.
- Γ, the reflection coefficient at the boundary.
7. Assignment: In the visible part of the electromagnetic spectrum, the index of refraction of
water is n = 1.33. What is the critical angle for light waves generated by an underwater light
source looking upward?
8. A light source is placed 1 meter below the water surface and radiates light isotropically in all
directions. The index of refraction of water is n = 1.33. Given the critical angle for light
traveling from water to air is θc = 48.8◦ , calculate the diameter of the circle illuminated on the
waters surface when viewed from above.
9. A beam of yellow light with wavelength λ1 = 0.6 µm is normally incident in air upon a glass
surface. The glass is sufficiently thick such that we can ignore its back surface. The surface is
located at the plane z = 0, and the relative permittivity of the glass is r = 2.25. Determine
the following:
(a) The locations of the electric field maxima in medium 1 (air).
(b) The standing-wave ratio.
(c) The fraction of the incident power transmitted into the glass medium.
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