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Find the Brewster angle of a wave transmitted from a medium of permittivity 4 to a medium of permittivity 2.
- a)35.26
- b)53.62
- c)26.35
- d)62.53
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Find the Brewster angle of a wave transmitted from a medium of permitt...
Answer: a
Explanation: The Brewster angle is given by θb = tan-1(n2/n1), where n = √ε. Thus we can express the formula in terms of permittivity as θb = tan-1√ (ε 2/ε 1). Here ε1 = 4 and ε2 = 2. Thus we get θb = tan-1√ (2/4) =
tan-1(0.707) = 35.26 degree.
Explanation: The Brewster angle is given by θb = tan-1(n2/n1), where n = √ε. Thus we can express the formula in terms of permittivity as θb = tan-1√ (ε 2/ε 1). Here ε1 = 4 and ε2 = 2. Thus we get θb = tan-1√ (2/4) =
tan-1(0.707) = 35.26 degree.
Most Upvoted Answer
Find the Brewster angle of a wave transmitted from a medium of permitt...
The Brewster angle is the angle of incidence at which light with a specific polarization (known as p-polarization) is perfectly transmitted through a surface with minimal reflection. It is given by the equation:
Brewster angle (θB) = arctan(n2/n1)
where n1 and n2 are the refractive indices of the two media.
In this case, we are given the permittivity (ε) of the two media instead of refractive indices. The refractive index (n) is related to the permittivity by the equation:
n = sqrt(ε)
Given that the permittivity of the first medium is 4 and the permittivity of the second medium is 2, we can calculate the refractive indices:
n1 = sqrt(4) = 2
n2 = sqrt(2) ≈ 1.414
Therefore, we can substitute these values into the Brewster angle equation:
θB = arctan(1.414/2)
Taking the arctan of this value gives us the Brewster angle:
θB ≈ 35.26 degrees
Therefore, option A is the correct answer.
To summarize:
- Permittivity of medium 1 (ε1) = 4
- Permittivity of medium 2 (ε2) = 2
Calculating refractive indices:
- Refractive index of medium 1 (n1) = sqrt(4) = 2
- Refractive index of medium 2 (n2) = sqrt(2) ≈ 1.414
Substituting values into Brewster angle equation:
- θB = arctan(1.414/2)
Calculating Brewster angle:
- θB ≈ 35.26 degrees.
Brewster angle (θB) = arctan(n2/n1)
where n1 and n2 are the refractive indices of the two media.
In this case, we are given the permittivity (ε) of the two media instead of refractive indices. The refractive index (n) is related to the permittivity by the equation:
n = sqrt(ε)
Given that the permittivity of the first medium is 4 and the permittivity of the second medium is 2, we can calculate the refractive indices:
n1 = sqrt(4) = 2
n2 = sqrt(2) ≈ 1.414
Therefore, we can substitute these values into the Brewster angle equation:
θB = arctan(1.414/2)
Taking the arctan of this value gives us the Brewster angle:
θB ≈ 35.26 degrees
Therefore, option A is the correct answer.
To summarize:
- Permittivity of medium 1 (ε1) = 4
- Permittivity of medium 2 (ε2) = 2
Calculating refractive indices:
- Refractive index of medium 1 (n1) = sqrt(4) = 2
- Refractive index of medium 2 (n2) = sqrt(2) ≈ 1.414
Substituting values into Brewster angle equation:
- θB = arctan(1.414/2)
Calculating Brewster angle:
- θB ≈ 35.26 degrees.
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Find the Brewster angle of a wave transmitted from a medium of permittivity 4 to a medium of permittivity 2.a)35.26b)53.62c)26.35d)62.53Correct answer is option 'A'. Can you explain this answer?
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