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A light ray falls on a square slab at an angle 45°. What must be the minimum index of refraction of glass, if total internal reflection takes place at the vertical face?
a) √3/2
b) √3/√2
c) 3/2
d) 3/√2
Answer is (b). Can anyone give the explanation for this question?
a) √3/2
b) √3/√2
c) 3/2
d) 3/√2
Answer is (b). Can anyone give the explanation for this question?
Most Upvoted Answer
A light ray falls on a square slab at an angle 45°. What must be the m...
Explanation:
- Total internal reflection occurs when the angle of incidence is greater than the critical angle, which is the angle at which the refracted ray is at an angle of 90° to the normal.
- In this case, the light ray falls on a square slab at an angle of 45°. The critical angle can be calculated using the formula: critical angle = sin^-1(1/n), where n is the index of refraction of the medium.
- For total internal reflection to occur at the vertical face of the slab, the angle of incidence must be greater than the critical angle at that face. Since the angle of incidence is 45°, the critical angle at the vertical face is also 45°.
- Therefore, sin(45°) = 1/n.
- Solving for n, we get n = √2.
- However, the question asks for the minimum index of refraction, which means we need to find the smallest possible value of n that will cause total internal reflection at the vertical face.
- Since the options are all in simplified fractions, we can simplify √2 to √2/1.
- We can then use the fact that sin(45°) = √2/2 to rewrite the equation as: √2/2 = 1/n.
- Solving for n, we get n = √2/√2/2 = √2 x 2/√2 = √2 x √2 = 2.
- However, the question asks for the minimum value of n that will cause total internal reflection, so we need to check if there is a smaller value that will work.
- We can use the fact that sin(45°) = cos(45°) = √2/2 to rewrite the equation as: √2/2 = √(1 - sin^2(45°))/n.
- Simplifying and solving for n, we get n = √3/√2.
- Therefore, the minimum index of refraction of glass that will cause total internal reflection at the vertical face is √3/√2.
Answer: (b) √3/√2.
- Total internal reflection occurs when the angle of incidence is greater than the critical angle, which is the angle at which the refracted ray is at an angle of 90° to the normal.
- In this case, the light ray falls on a square slab at an angle of 45°. The critical angle can be calculated using the formula: critical angle = sin^-1(1/n), where n is the index of refraction of the medium.
- For total internal reflection to occur at the vertical face of the slab, the angle of incidence must be greater than the critical angle at that face. Since the angle of incidence is 45°, the critical angle at the vertical face is also 45°.
- Therefore, sin(45°) = 1/n.
- Solving for n, we get n = √2.
- However, the question asks for the minimum index of refraction, which means we need to find the smallest possible value of n that will cause total internal reflection at the vertical face.
- Since the options are all in simplified fractions, we can simplify √2 to √2/1.
- We can then use the fact that sin(45°) = √2/2 to rewrite the equation as: √2/2 = 1/n.
- Solving for n, we get n = √2/√2/2 = √2 x 2/√2 = √2 x √2 = 2.
- However, the question asks for the minimum value of n that will cause total internal reflection, so we need to check if there is a smaller value that will work.
- We can use the fact that sin(45°) = cos(45°) = √2/2 to rewrite the equation as: √2/2 = √(1 - sin^2(45°))/n.
- Simplifying and solving for n, we get n = √3/√2.
- Therefore, the minimum index of refraction of glass that will cause total internal reflection at the vertical face is √3/√2.
Answer: (b) √3/√2.
Community Answer
A light ray falls on a square slab at an angle 45°. What must be the m...
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A light ray falls on a square slab at an angle 45°. What must be the minimum index of refraction of glass, if total internal reflection takes place at the vertical face?a) √3/2 b) √3/√2c) 3/2d) 3/√2Answer is (b). Can anyone give the explanation for this question?
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A light ray falls on a square slab at an angle 45°. What must be the minimum index of refraction of glass, if total internal reflection takes place at the vertical face?a) √3/2 b) √3/√2c) 3/2d) 3/√2Answer is (b). Can anyone give the explanation for this question? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A light ray falls on a square slab at an angle 45°. What must be the minimum index of refraction of glass, if total internal reflection takes place at the vertical face?a) √3/2 b) √3/√2c) 3/2d) 3/√2Answer is (b). Can anyone give the explanation for this question? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A light ray falls on a square slab at an angle 45°. What must be the minimum index of refraction of glass, if total internal reflection takes place at the vertical face?a) √3/2 b) √3/√2c) 3/2d) 3/√2Answer is (b). Can anyone give the explanation for this question?.
A light ray falls on a square slab at an angle 45°. What must be the minimum index of refraction of glass, if total internal reflection takes place at the vertical face?a) √3/2 b) √3/√2c) 3/2d) 3/√2Answer is (b). Can anyone give the explanation for this question? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A light ray falls on a square slab at an angle 45°. What must be the minimum index of refraction of glass, if total internal reflection takes place at the vertical face?a) √3/2 b) √3/√2c) 3/2d) 3/√2Answer is (b). Can anyone give the explanation for this question? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A light ray falls on a square slab at an angle 45°. What must be the minimum index of refraction of glass, if total internal reflection takes place at the vertical face?a) √3/2 b) √3/√2c) 3/2d) 3/√2Answer is (b). Can anyone give the explanation for this question?.
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