GATE EC 2018 Set 1 — Question 59
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Electromagnetics → Plane Waves → Brewster & Total Internal Reflection
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Question
A uniform plane wave traveling in free space and having the electric fieldis incident on a dielectric medium (relative permittivity , relative permeability ) as shown in the figure and there is no reflected wave.
The relative permittivity (correct to two decimal places) of the dielectric medium is __________.
Correct answer
1.9 to 2.1
Solution
The given electric field is .
Thus, .
The angle of incidence is the angle between and the normal :
.
Then, .
Given medium 1 is free space () and medium 2 is the dielectric ():
.
1.Identify the wave vector ():
From the phase term , we have:Thus, .
2.Calculate the magnitude of ():
.3.Determine the angle of incidence ():
From the diagram, the interface is the -axis (), so the normal to the interface is the -axis (). The angle of incidence is the angle between and the normal :
.
Then, .
4.Identify the polarization:
The plane of incidence is the - plane. The electric field vector also lies in the - plane. Therefore, the wave is parallel polarized (TM wave).5.Apply the Brewster angle condition:
For a parallel polarized wave, there is no reflection when the angle of incidence equals the Brewster angle ():Given medium 1 is free space () and medium 2 is the dielectric ():
.
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