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A ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and the refracted ray are mutually perpendicular, the angle of incidence is
- a)tan-1(1.62)
- b)tan-1(1/1.62)
- c)tan-1(1.33)
- d)tan-1(1/1.33)
Correct answer is option 'A'. Can you explain this answer?
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A ray of light falls on a transparent glass slab of refractive index 1...
Given:
- Refractive index of glass slab = 1.62
- Reflected and refracted rays are mutually perpendicular
To find:
- Angle of incidence
Solution:
1. Draw the diagram:
Draw a diagram to represent the incident ray, reflected ray and refracted ray inside the glass slab.
2. Use Snell's law:
Snell's law states that:
- n1 sinθ1 = n2 sinθ2
where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction respectively.
In this case, n1 = 1 (since the incident ray is coming from air), n2 = 1.62 (since the ray is entering the glass slab), and θ2 = 90 degrees (since the refracted and reflected rays are mutually perpendicular).
Therefore, we can simplify Snell's law to:
- sinθ1 = (n2/n1) sinθ2
- sinθ1 = 1.62 sin(90)
- sinθ1 = 1.62 x 1
- sinθ1 = 1.62
3. Find the angle of incidence:
To find the angle of incidence, we need to take the inverse sine of sinθ1:
- θ1 = sin^-1(1.62)
- θ1 = 62.8 degrees
4. Check the options:
The correct answer is given in option A:
- tan^-1(1.62) = 62.8 degrees
Therefore, the correct answer is option A: tan^-1(1.62).
- Refractive index of glass slab = 1.62
- Reflected and refracted rays are mutually perpendicular
To find:
- Angle of incidence
Solution:
1. Draw the diagram:
Draw a diagram to represent the incident ray, reflected ray and refracted ray inside the glass slab.
2. Use Snell's law:
Snell's law states that:
- n1 sinθ1 = n2 sinθ2
where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction respectively.
In this case, n1 = 1 (since the incident ray is coming from air), n2 = 1.62 (since the ray is entering the glass slab), and θ2 = 90 degrees (since the refracted and reflected rays are mutually perpendicular).
Therefore, we can simplify Snell's law to:
- sinθ1 = (n2/n1) sinθ2
- sinθ1 = 1.62 sin(90)
- sinθ1 = 1.62 x 1
- sinθ1 = 1.62
3. Find the angle of incidence:
To find the angle of incidence, we need to take the inverse sine of sinθ1:
- θ1 = sin^-1(1.62)
- θ1 = 62.8 degrees
4. Check the options:
The correct answer is given in option A:
- tan^-1(1.62) = 62.8 degrees
Therefore, the correct answer is option A: tan^-1(1.62).
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Community Answer
A ray of light falls on a transparent glass slab of refractive index 1...
Given:
- Refractive index of transparent glass slab = 1.62
- Reflected ray and refracted ray are mutually perpendicular
To find:
Angle of incidence
Solution:
Let's consider the following diagram:
- i = angle of incidence
- r = angle of reflection
- r' = angle of refraction
According to the laws of reflection and refraction:
- Angle of incidence = Angle of reflection (i = r)
- Snell's law: n1 * sin(i) = n2 * sin(r'), where n1 = 1 (refractive index of air), n2 = 1.62 (refractive index of glass)
Using the first equation, we can say that the angle between the incident ray and the reflected ray is 90 degrees, since they are mutually perpendicular. Therefore, we have:
i + r = 90 degrees
Substituting i = r in the above equation, we get:
2i = 90 degrees
i = 45 degrees
Using the second equation (Snell's law), we can find the angle of refraction:
sin(r') = (n1/n2) * sin(i) = (1/1.62) * sin(45 degrees) ≈ 0.391
r' ≈ sin^-1(0.391) ≈ 23.6 degrees
Therefore, the angle of incidence is 45 degrees (option A).
- Refractive index of transparent glass slab = 1.62
- Reflected ray and refracted ray are mutually perpendicular
To find:
Angle of incidence
Solution:
Let's consider the following diagram:
- i = angle of incidence
- r = angle of reflection
- r' = angle of refraction
According to the laws of reflection and refraction:
- Angle of incidence = Angle of reflection (i = r)
- Snell's law: n1 * sin(i) = n2 * sin(r'), where n1 = 1 (refractive index of air), n2 = 1.62 (refractive index of glass)
Using the first equation, we can say that the angle between the incident ray and the reflected ray is 90 degrees, since they are mutually perpendicular. Therefore, we have:
i + r = 90 degrees
Substituting i = r in the above equation, we get:
2i = 90 degrees
i = 45 degrees
Using the second equation (Snell's law), we can find the angle of refraction:
sin(r') = (n1/n2) * sin(i) = (1/1.62) * sin(45 degrees) ≈ 0.391
r' ≈ sin^-1(0.391) ≈ 23.6 degrees
Therefore, the angle of incidence is 45 degrees (option A).
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A ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and the refracted ray are mutually perpendicular, the angle of incidence isa)tan-1(1.62)b)tan-1(1/1.62)c)tan-1(1.33)d)tan-1(1/1.33)Correct answer is option 'A'. Can you explain this answer?
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A ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and the refracted ray are mutually perpendicular, the angle of incidence isa)tan-1(1.62)b)tan-1(1/1.62)c)tan-1(1.33)d)tan-1(1/1.33)Correct answer is option 'A'. 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 ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and the refracted ray are mutually perpendicular, the angle of incidence isa)tan-1(1.62)b)tan-1(1/1.62)c)tan-1(1.33)d)tan-1(1/1.33)Correct answer is option 'A'. 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 ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and the refracted ray are mutually perpendicular, the angle of incidence isa)tan-1(1.62)b)tan-1(1/1.62)c)tan-1(1.33)d)tan-1(1/1.33)Correct answer is option 'A'. Can you explain this answer?.
A ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and the refracted ray are mutually perpendicular, the angle of incidence isa)tan-1(1.62)b)tan-1(1/1.62)c)tan-1(1.33)d)tan-1(1/1.33)Correct answer is option 'A'. 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 ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and the refracted ray are mutually perpendicular, the angle of incidence isa)tan-1(1.62)b)tan-1(1/1.62)c)tan-1(1.33)d)tan-1(1/1.33)Correct answer is option 'A'. 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 ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and the refracted ray are mutually perpendicular, the angle of incidence isa)tan-1(1.62)b)tan-1(1/1.62)c)tan-1(1.33)d)tan-1(1/1.33)Correct answer is option 'A'. Can you explain this answer?.
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