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Concept explainers
(a)
Find incidence angle.
(a)
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Answer to Problem 75P
The incidence angle is
Explanation of Solution
Calculation:
Consider the expression to find the incidence angle.
Rearrange the expression for incidence angle.
Consider the expression to find
Here,
From the given electric field, the propagation vector is
Substitute
From the given data,
Substitute
Conclusion:
Thus, the incidence angle is
(b)
Find the time-average power in air.
(b)
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Answer to Problem 75P
The time-average power in air is
Explanation of Solution
Calculation:
Consider the expression to find the time-average power in air.
Here,
Find
Substitute
Conclusion:
Thus, the time-average power in air is
(c)
Find the reflected and transmitted electric fields.
(c)
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Answer to Problem 75P
The reflected and transmitted electric fields are
Explanation of Solution
Calculation:
Consider the expression for reflected electric field for the given data.
The reflection angle is equal to incidence angle. Therefore,
Consider the expression of reflection coefficient in the parallel polarization of oblique incidence.
Here,
Rewrite Equation (5) for the given data.
As
Rearrange the expression for
Consider the expression to find the angle of transmission
Rewrite the expression for the given data.
Rearrange the expression to find the angle of transmission
Substitute
Substitute
From the given Figure, find
From the given Figure, find
Substitute
Consider the expression for transmitted electric field.
Consider the expression of transmission coefficient in the parallel polarization of oblique incidence.
Rewrite the expression for the given data.
As
Rearrange the expression for
Substitute
From the given Figure, find
Find
Find
Find the value of
Simplify the expression.
Substitute 10 for
From the given Figure, find
Substitute
Conclusion:
Thus, the reflected and transmitted electric fields are
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Chapter 10 Solutions
Elements of Electromagnetics
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