A plane wave traveling in a non-magnetic medium with dielectric constant of 4 is

Question

A plane wave traveling in a non-magnetic medium with dielectric constant of 4 is obliquely incident upon the interface at z = 0 with vacuum. situation is depicted in the inset of the figure below. Also shown are plots of reflection coefficient versus incident angle generated using the appropriate equations in MATLAB. What is the value of, the reflection coefficient at normal incidence? Type your answer to three places after the decimal, i.e, in the form x.xxx. _______ Match the correct phrase to the correct quantity. _______ The reflection coefficient for parallel polarization versus incident angle. Curve 2. _______ The reflection coefficient for perpendicular polarization versus incident angle. Curve 1. _______ Critical angle. Angle theta _2 _______ Brewster angle. Angle theta _1 What is the value of theta _1? Type your answer in degrees to one place after the decimal, i.e., xx.x. _______ What is the value of theta _2? Type your answer in degrees to one place after the decimal, i.e., xx.x. _______

Explanation / Answer

A plane wave is travelling in a non-magnetic medium with dielectric constant 4*0 is incident upon the interface at z=0 with vacuum.

Basically the plane wave is travelling from denser to rarer medium. Then the total internal reflection takes place only when the angle of incidence is greater than or equal to the critical angle.

Now to calculate the reflection coefficient which can be defined as the ratio of the reflected to incident tangential component, can be expressed as;

Ref.Cof = (1- 2)/ (1+2)

Where 1 is the dielectric constant of the denser medium and 2 is the dielectric constant of the rarer medium.

Therefore at normal incidence;

Ref.Cof = (4*0- 0)/ (4*0+ 0) = 3/5 = 0.6.

The reflection coefficient for parallel polarization versus incident angle – curve 1

The reflection coefficient for perpendicular polarization versus incident angle – curve 2

Critical Angle – angle 1.

Brewster Angle – angle 2.

To find the critical angle; if we remember the Snell’s law in optics; the formula will be;

Sin(1)=squareroot(2/ 1) = ½

1 = 300.

At 2, the total internal reflection condition is occurred. Hence 2 will be any angle greater than 300.

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