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Unpolarised light is incident on a plane glass sheet of refractive index 1.34. What should be the angle of incident ray so that reflected and refracted rays are perpendicular to each other.
(1) 37°
(2) 53°
(3) 58°
(4) 60°?
(1) 37°
(2) 53°
(3) 58°
(4) 60°?
Most Upvoted Answer
Unpolarised light is incident on a plane glass sheet of refractive ind...
Understanding the Problem
When unpolarised light strikes a plane glass sheet, we need to find the angle of incidence where the reflected and refracted rays are perpendicular to each other.
Conditions for Perpendicular Rays
- For the reflected and refracted rays to be perpendicular, the angle of reflection (r) and the angle of refraction (R) must satisfy the condition:
r + R = 90°
This leads to the relationship:
R = 90° - r
Applying Snell's Law
- Snell's Law states:
n1 * sin(i) = n2 * sin(R)
Where:
- n1 = refractive index of the first medium (air, approximately 1)
- n2 = refractive index of glass (1.34)
- i = angle of incidence
- R = angle of refraction
- Since R = 90° - r, we can replace R in Snell's Law:
sin(R) = cos(r)
Finding the Angle of Incidence
- From the relationship:
n1 * sin(i) = n2 * cos(r)
We know that r = i (due to the law of reflection).
- This transforms to:
sin(i) = 1.34 * cos(i)
Solving the Equation
- This equation can be solved using trigonometric identities or numerical methods to find the angle of incidence (i).
Conclusion
After calculating, the angle of incidence that satisfies the condition is:
- Angle of Incidence = 53° (Option 2)
This angle ensures that the reflected and refracted rays are indeed perpendicular to each other.
When unpolarised light strikes a plane glass sheet, we need to find the angle of incidence where the reflected and refracted rays are perpendicular to each other.
Conditions for Perpendicular Rays
- For the reflected and refracted rays to be perpendicular, the angle of reflection (r) and the angle of refraction (R) must satisfy the condition:
r + R = 90°
This leads to the relationship:
R = 90° - r
Applying Snell's Law
- Snell's Law states:
n1 * sin(i) = n2 * sin(R)
Where:
- n1 = refractive index of the first medium (air, approximately 1)
- n2 = refractive index of glass (1.34)
- i = angle of incidence
- R = angle of refraction
- Since R = 90° - r, we can replace R in Snell's Law:
sin(R) = cos(r)
Finding the Angle of Incidence
- From the relationship:
n1 * sin(i) = n2 * cos(r)
We know that r = i (due to the law of reflection).
- This transforms to:
sin(i) = 1.34 * cos(i)
Solving the Equation
- This equation can be solved using trigonometric identities or numerical methods to find the angle of incidence (i).
Conclusion
After calculating, the angle of incidence that satisfies the condition is:
- Angle of Incidence = 53° (Option 2)
This angle ensures that the reflected and refracted rays are indeed perpendicular to each other.
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Unpolarised light is incident on a plane glass sheet of refractive index 1.34. What should be the angle of incident ray so that reflected and refracted rays are perpendicular to each other.(1) 37°(2) 53°(3) 58°(4) 60°?
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Unpolarised light is incident on a plane glass sheet of refractive index 1.34. What should be the angle of incident ray so that reflected and refracted rays are perpendicular to each other.(1) 37°(2) 53°(3) 58°(4) 60°? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Unpolarised light is incident on a plane glass sheet of refractive index 1.34. What should be the angle of incident ray so that reflected and refracted rays are perpendicular to each other.(1) 37°(2) 53°(3) 58°(4) 60°? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Unpolarised light is incident on a plane glass sheet of refractive index 1.34. What should be the angle of incident ray so that reflected and refracted rays are perpendicular to each other.(1) 37°(2) 53°(3) 58°(4) 60°?.
Unpolarised light is incident on a plane glass sheet of refractive index 1.34. What should be the angle of incident ray so that reflected and refracted rays are perpendicular to each other.(1) 37°(2) 53°(3) 58°(4) 60°? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Unpolarised light is incident on a plane glass sheet of refractive index 1.34. What should be the angle of incident ray so that reflected and refracted rays are perpendicular to each other.(1) 37°(2) 53°(3) 58°(4) 60°? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Unpolarised light is incident on a plane glass sheet of refractive index 1.34. What should be the angle of incident ray so that reflected and refracted rays are perpendicular to each other.(1) 37°(2) 53°(3) 58°(4) 60°?.
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