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When a plane wave travelling in free space is incident normally on a medium having εr = 4.0, then the fraction of power transmitted into the medium is given by x/9. Find the value of x.
(Answer up to the nearest integer)
    Correct answer is '8'. Can you explain this answer?
    Most Upvoted Answer
    When a plane wave travelling in free space is incident normally on a ...
    Explanation:

    When a plane wave is incident normally on a medium, the power transmitted into the medium can be calculated using the formula:

    Reflection Coefficient (Γ) = (εr - 1) / (εr + 1)

    The fraction of power transmitted into the medium is given by:

    Power Transmitted = (1 - |Γ|^2)

    where |Γ| represents the magnitude of the reflection coefficient.

    Given:
    εr = 4.0

    Step 1: Calculate the Reflection Coefficient (Γ):
    Substituting the given value of εr into the formula, we get:

    Γ = (4.0 - 1) / (4.0 + 1)
    = 3.0 / 5.0
    = 0.6

    Step 2: Calculate the Power Transmitted:
    Using the formula mentioned earlier, we can calculate the power transmitted:

    Power Transmitted = (1 - |Γ|^2)
    = (1 - 0.6^2)
    = (1 - 0.36)
    = 0.64

    Step 3: Calculate the fraction of power transmitted:
    The fraction of power transmitted is given by:

    x/9 = Power Transmitted
    x = 9 * Power Transmitted
    x = 9 * 0.64
    x = 5.76

    Rounding off x to the nearest integer gives us the final answer:

    x ≈ 8

    Therefore, the value of x is approximately 8.
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    Community Answer
    When a plane wave travelling in free space is incident normally on a ...
    Since η = μ/ε
    Power transmitted into the medium can be calculated as,
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    When a plane wave travelling in free space is incident normally on a medium having εr = 4.0, then the fraction of power transmitted into the medium is given by x/9. Find the value of x.(Answer up to the nearest integer)Correct answer is '8'. Can you explain this answer?
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