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A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is √3, then the angle of incidence is :-
- a)30°
- b)45°
- c)90°
- d)60°
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A monochromatic light is incident at a certain angle on an equilateral...
i = e
by Snell's law
i = 60
by Snell's law
i = 60
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A monochromatic light is incident at a certain angle on an equilateral...
To find the refractive index of the material of the prism, we can use the formula for minimum deviation:
sin((A + D)/2) / sin(A/2) = n
Where A is the angle of incidence and D is the angle of deviation.
Since the prism is equilateral, each angle of the prism is 60 degrees.
Let's assume the angle of incidence is 30 degrees (half of the angle of the prism).
sin((30 + D)/2) / sin(30/2) = n
sin(15 + D/2) / sin(15) = n
Since the light suffers minimum deviation, the angle of deviation is also 30 degrees (equal to the angle of incidence).
sin(15 + 30/2) / sin(15) = n
sin(15 + 15) / sin(15) = n
sin(30) / sin(15) = n
Using the identity sin(2x) = 2sin(x)cos(x), we can rewrite the equation as:
2sin(15)cos(15) / sin(15) = n
2cos(15) = n
Using a calculator, we can find the value of cos(15) ≈ 0.9659.
n ≈ 2 * 0.9659
n ≈ 1.9318
Therefore, the refractive index of the material of the prism is approximately 1.9318.
sin((A + D)/2) / sin(A/2) = n
Where A is the angle of incidence and D is the angle of deviation.
Since the prism is equilateral, each angle of the prism is 60 degrees.
Let's assume the angle of incidence is 30 degrees (half of the angle of the prism).
sin((30 + D)/2) / sin(30/2) = n
sin(15 + D/2) / sin(15) = n
Since the light suffers minimum deviation, the angle of deviation is also 30 degrees (equal to the angle of incidence).
sin(15 + 30/2) / sin(15) = n
sin(15 + 15) / sin(15) = n
sin(30) / sin(15) = n
Using the identity sin(2x) = 2sin(x)cos(x), we can rewrite the equation as:
2sin(15)cos(15) / sin(15) = n
2cos(15) = n
Using a calculator, we can find the value of cos(15) ≈ 0.9659.
n ≈ 2 * 0.9659
n ≈ 1.9318
Therefore, the refractive index of the material of the prism is approximately 1.9318.
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A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractiveindex of the material of the prism is√3,then the angle of incidence is :-a)30°b)45°c)90°d)60°Correct answer is option 'D'. Can you explain this answer?
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A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractiveindex of the material of the prism is√3,then the angle of incidence is :-a)30°b)45°c)90°d)60°Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractiveindex of the material of the prism is√3,then the angle of incidence is :-a)30°b)45°c)90°d)60°Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractiveindex of the material of the prism is√3,then the angle of incidence is :-a)30°b)45°c)90°d)60°Correct answer is option 'D'. Can you explain this answer?.
A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractiveindex of the material of the prism is√3,then the angle of incidence is :-a)30°b)45°c)90°d)60°Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractiveindex of the material of the prism is√3,then the angle of incidence is :-a)30°b)45°c)90°d)60°Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractiveindex of the material of the prism is√3,then the angle of incidence is :-a)30°b)45°c)90°d)60°Correct answer is option 'D'. Can you explain this answer?.
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