# Antennas Questions and Answers – Radio Wave Propagation – Reflection Factor for Parallel Propagation

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This set of Antennas Problems focuses on “Radio Wave Propagation – Reflection Factor for Parallel Propagation”.

1. The reflection factor is given by the ratio of ____________
a) Reflected wave to incident wave
b) Incident wave to reflected wave
c) Sum of reflected and incident waves to difference of reflected and incident waves
d) Difference of reflected and incident waves to sum of reflected and incident waves

Explanation: The reflection factor is given by the ratio of Reflected wave to incident wave.
$$ρ=\frac{reflected \,wave}{incident\, wave}=\frac{E_r}{E_i}$$
ρ=1 It means that surface is perfect reflecting medium.

2. What is the reflection coefficient for a perfect reflecting surface?
a) 1
b) 0
c) <1
d) >1

Explanation: The reflection factor is defined as the ratio of Reflected wave to incident wave.
$$ρ=\frac{reflected \,wave}{incident \,wave}=\frac{E_r}{E_i}$$
For a perfect reflecting surface, total incident waves are reflected completely. Er = Ei
$$ρ=\frac{E_r}{E_i}=1.$$

3. What is the reflection coefficient if there are no any reflections?
a) 1
b) 0
c) <1
d) >1

Explanation: The reflection factor is given by the ratio of Reflected wave to incident wave.
$$ρ=\frac{reflected \,wave}{incident \,wave}=\frac{E_r}{E_i}$$
No reflections means Er = 0 =>ρ = 0
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4. Which of the following holds true for Brewster angle?
a) It is about the angle of reflection
b) It is the angle of incident at which no reflections occur
c) It is the angle of incident at which maximum reflections occur
d) It is about the angle of refraction

Explanation: Brewster angle is defined as the angle of incident at which no reflections occurs.
$$θ=tan^{-1}⁡\sqrt{\frac{ϵ_{r2}}{ϵ_{r1}}}$$

5. Reflection coefficient of plane waves with normal incidence in terms of impedances of medium is ____
a) $$γ_r=\frac{η_2-η_1}{η_2+η_1}$$
b) $$γ_r=\frac{2η_2}{η_2+η_1}$$
c) $$γ_r=\frac{2η_1}{η_2+η_1}$$
d) $$γ_r=\frac{η_2+η_1}{η_2-η_1}$$

Explanation: The reflection factor is given by the ratio of Reflected wave to incident wave.
$$ρ=\frac{reflected\, wave}{incident\, wave}=\frac{E_r}{E_i}$$
Reflection coefficient of plane waves with normal incidence in terms of impedances of medium is $$γ_r=\frac{η_2-η_1}{η_2+η_1}$$
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6. Relation between transmission coefficient γt and reflection coefficient is γr is
a) γr= γt-1
b) γr= γt+1
c) γr= γt-2
d) γr= (γt-1) / γt+1

Explanation: Relation between transmission coefficient γt and reflection coefficient is γr is γr = γt – 1
Transmission coefficient is the ratio of transmitted to incident wave. The reflection factor is given by the ratio of Reflected wave to incident wave.

7. Transmission coefficient of a plane wave with normal incidence is _________
a) $$γ_t=\frac{2η_2}{η_2+η_1}$$
b) $$γ_t=\frac{η_2}{η_2+η_1}$$
c) $$γ_t=\frac{2η_2}{η_2+η_1}$$
d) $$γ_r=\frac{η_2-η_1}{η_2+η_1}$$

Explanation: Transmission coefficient is the ratio of transmitted to incident wave. Relation between transmission coefficient γt and reflection coefficient is γr is γr = γt-1.
So the Transmission coefficient of a plane wave with normal incidence is $$γ_t=\frac{2η_2}{η_2+η_1}$$

8. Complex dielectric constant of earth is given by ____
a) $$ϵ’=ϵ+\frac{σ}{jw}$$
b) $$ϵ’=σϵ+\frac{1}{jw}$$
c) $$ϵ’=σ+\frac{ϵ}{jw}$$
d) $$ϵ’=ϵ+\frac{σϵ}{jw}$$

Explanation: The earth is neither a good conductor nor a good dielectric. So the dielectric constant of earth is complex and is given by $$ϵ’=ϵ+\frac{σ}{jw}$$where σ is the conductivity and w is angular frequency.

9. Which of the following is the expression for tilt angle?
a) $$θ=1/2 tan^{-1}⁡(\frac{σ}{ωϵ})$$
b) $$θ=2 tan^{-1}⁡(\frac{σ}{ωϵ})$$
c) $$θ=1/2 tan^{-1}⁡(\frac{σϵ}{ω})$$
d) $$θ=2 tan^{-1}⁡(\frac{wϵ}{σ})$$

Explanation: The wave tilt of the surface wave depends on the conductivity of earth, permittivity and angular frequency of the waves. Expression for tilt angle is $$θ=1/2 tan^{-1}⁡(\frac{σ}{ωϵ}).$$

10. Find the tilt angle of the radio wave with 1MHz frequency and conductivity of earth is 5 ×10-3S/m and relative permittivity 10?
a) 41.8°
b) 83.6°
c) 48.1°
d) 38.6°

Explanation: Expression for tilt angle is $$θ=1/2 tan^{-1}⁡(\frac{σ}{ωϵ}).$$
$$=0.5 tan^{-1}⁡(\frac{5 ×10^{-3}}{2π×10^6×10×(\frac{1}{36π}) 10^{-9}})≈41.8°$$

11. Brewster angle doesn’t exist for perpendicular polarization.
a) True
b) False

Explanation: Brewster angle is defined as the angle of incident at which no reflections occurs.
$$θ=tan^{-1}⁡\sqrt{\frac{ϵ_{r2}}{ϵ_{r1}}}$$
At θ =90, tan θ=∞, which doesn’t exist in reality.

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