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The critical angle for two media with permittivities of 16 and 9 respectively is
- a)48.59
- b)54.34
- c)60
- d)45
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The critical angle for two media with permittivities of 16 and 9 respe...
Answer: a
Explanation: The sine of the critical angle is the ratio of refractive index of medium 2 to that in medium 1. Thus sin θc = n2/n1. Also n = √ε, thus sin θc = √ε2/√ε1. Put ε1 = 16 and ε2 = 9, we get θc = sin-1(3/4) = 48.59 degree.
Explanation: The sine of the critical angle is the ratio of refractive index of medium 2 to that in medium 1. Thus sin θc = n2/n1. Also n = √ε, thus sin θc = √ε2/√ε1. Put ε1 = 16 and ε2 = 9, we get θc = sin-1(3/4) = 48.59 degree.
Most Upvoted Answer
The critical angle for two media with permittivities of 16 and 9 respe...
The critical angle is an important concept in optics and is defined as the angle of incidence at which the refracted ray in a medium is at an angle of 90 degrees with the normal to the surface separating the two media. It occurs when light travels from a medium with higher refractive index to a medium with a lower refractive index.
Given that the permittivities of the two media are 16 and 9, we can use the relationship between permittivity and refractive index to calculate the critical angle.
1. Relationship between permittivity and refractive index:
The refractive index (n) of a medium is related to the permittivity (ε) of the medium by the equation:
n = √ε
2. Calculation of refractive indices:
Using the given permittivities, we can calculate the refractive indices of the two media:
For medium 1: n1 = √16 = 4
For medium 2: n2 = √9 = 3
3. Calculation of critical angle:
The critical angle (θc) can be calculated using the following formula:
θc = sin^(-1)(n2/n1)
Substituting the values of n1 and n2, we have:
θc = sin^(-1)(3/4)
Using a scientific calculator, we can calculate the inverse sine of 3/4, which gives us the critical angle:
θc ≈ 48.59 degrees
Therefore, the correct answer is option A) 48.59 degrees.
Given that the permittivities of the two media are 16 and 9, we can use the relationship between permittivity and refractive index to calculate the critical angle.
1. Relationship between permittivity and refractive index:
The refractive index (n) of a medium is related to the permittivity (ε) of the medium by the equation:
n = √ε
2. Calculation of refractive indices:
Using the given permittivities, we can calculate the refractive indices of the two media:
For medium 1: n1 = √16 = 4
For medium 2: n2 = √9 = 3
3. Calculation of critical angle:
The critical angle (θc) can be calculated using the following formula:
θc = sin^(-1)(n2/n1)
Substituting the values of n1 and n2, we have:
θc = sin^(-1)(3/4)
Using a scientific calculator, we can calculate the inverse sine of 3/4, which gives us the critical angle:
θc ≈ 48.59 degrees
Therefore, the correct answer is option A) 48.59 degrees.
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The critical angle for two media with permittivities of 16 and 9 respectively isa)48.59b)54.34c)60d)45Correct answer is option 'A'. Can you explain this answer?
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The critical angle for two media with permittivities of 16 and 9 respectively isa)48.59b)54.34c)60d)45Correct answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The critical angle for two media with permittivities of 16 and 9 respectively isa)48.59b)54.34c)60d)45Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The critical angle for two media with permittivities of 16 and 9 respectively isa)48.59b)54.34c)60d)45Correct answer is option 'A'. Can you explain this answer?.
The critical angle for two media with permittivities of 16 and 9 respectively isa)48.59b)54.34c)60d)45Correct answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The critical angle for two media with permittivities of 16 and 9 respectively isa)48.59b)54.34c)60d)45Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The critical angle for two media with permittivities of 16 and 9 respectively isa)48.59b)54.34c)60d)45Correct answer is option 'A'. Can you explain this answer?.
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