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A transparent solid cylindrical rod has a refractive index of 2/√3 .it is surrounded by air .a light ray is incident at the midpoint of one end of the rod . The incident angle Tita for which the light ray grazes along the wall of the rod is. A) sin^-1 (√3/2) b)sin^-1(2/√3) C) sin^-1 (1/√3). D) sin^-1(1/2)?
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A transparent solid cylindrical rod has a refractive index of 2/√3 .it...
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A transparent solid cylindrical rod has a refractive index of 2/√3 .it...
Given:
- Refractive index of the solid cylindrical rod, n = 2/√3
- The rod is surrounded by air
To find:
The incident angle θ at which the light ray grazes along the wall of the rod.
Solution:
1. Understanding the problem:
When a light ray passes through a medium with a different refractive index, it changes its direction. This phenomenon is known as refraction. The angle at which the light ray is incident on the surface of the medium is called the incident angle. The angle between the refracted ray and the normal to the surface is called the angle of refraction.
2. Snell's Law:
Snell's law relates the incident angle (θ1), the refractive index of the first medium (n1), the angle of refraction (θ2), and the refractive index of the second medium (n2). It is given by:
n1 * sin(θ1) = n2 * sin(θ2)
3. Incident angle for grazing:
When the light ray grazes along the wall of the rod, it means that the angle of refraction is 90 degrees. Therefore, sin(θ2) = 1.
4. Applying Snell's Law:
In this case, the first medium is air with a refractive index of 1, and the second medium is the rod with a refractive index of 2/√3. Let's substitute the values into Snell's law:
1 * sin(θ1) = (2/√3) * 1
Simplifying further:
sin(θ1) = 2/√3
5. Finding the incident angle:
To find the incident angle θ1, we need to take the inverse sine (sin^-1) of both sides of the equation:
θ1 = sin^-1(2/√3)
6. Simplifying the answer:
To simplify the answer, we can rationalize the denominator:
θ1 = sin^-1(2/√3) * (√3/√3)
θ1 = sin^-1(2√3/3)
Therefore, the answer is option C) sin^-1(1/√3).
Summary:
The incident angle θ for which the light ray grazes along the wall of the rod is sin^-1(1/√3), which is option C) in the given choices.
- Refractive index of the solid cylindrical rod, n = 2/√3
- The rod is surrounded by air
To find:
The incident angle θ at which the light ray grazes along the wall of the rod.
Solution:
1. Understanding the problem:
When a light ray passes through a medium with a different refractive index, it changes its direction. This phenomenon is known as refraction. The angle at which the light ray is incident on the surface of the medium is called the incident angle. The angle between the refracted ray and the normal to the surface is called the angle of refraction.
2. Snell's Law:
Snell's law relates the incident angle (θ1), the refractive index of the first medium (n1), the angle of refraction (θ2), and the refractive index of the second medium (n2). It is given by:
n1 * sin(θ1) = n2 * sin(θ2)
3. Incident angle for grazing:
When the light ray grazes along the wall of the rod, it means that the angle of refraction is 90 degrees. Therefore, sin(θ2) = 1.
4. Applying Snell's Law:
In this case, the first medium is air with a refractive index of 1, and the second medium is the rod with a refractive index of 2/√3. Let's substitute the values into Snell's law:
1 * sin(θ1) = (2/√3) * 1
Simplifying further:
sin(θ1) = 2/√3
5. Finding the incident angle:
To find the incident angle θ1, we need to take the inverse sine (sin^-1) of both sides of the equation:
θ1 = sin^-1(2/√3)
6. Simplifying the answer:
To simplify the answer, we can rationalize the denominator:
θ1 = sin^-1(2/√3) * (√3/√3)
θ1 = sin^-1(2√3/3)
Therefore, the answer is option C) sin^-1(1/√3).
Summary:
The incident angle θ for which the light ray grazes along the wall of the rod is sin^-1(1/√3), which is option C) in the given choices.
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A transparent solid cylindrical rod has a refractive index of 2/√3 .it is surrounded by air .a light ray is incident at the midpoint of one end of the rod . The incident angle Tita for which the light ray grazes along the wall of the rod is. A) sin^-1 (√3/2) b)sin^-1(2/√3) C) sin^-1 (1/√3). D) sin^-1(1/2)?
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A transparent solid cylindrical rod has a refractive index of 2/√3 .it is surrounded by air .a light ray is incident at the midpoint of one end of the rod . The incident angle Tita for which the light ray grazes along the wall of the rod is. A) sin^-1 (√3/2) b)sin^-1(2/√3) C) sin^-1 (1/√3). D) sin^-1(1/2)? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A transparent solid cylindrical rod has a refractive index of 2/√3 .it is surrounded by air .a light ray is incident at the midpoint of one end of the rod . The incident angle Tita for which the light ray grazes along the wall of the rod is. A) sin^-1 (√3/2) b)sin^-1(2/√3) C) sin^-1 (1/√3). D) sin^-1(1/2)? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A transparent solid cylindrical rod has a refractive index of 2/√3 .it is surrounded by air .a light ray is incident at the midpoint of one end of the rod . The incident angle Tita for which the light ray grazes along the wall of the rod is. A) sin^-1 (√3/2) b)sin^-1(2/√3) C) sin^-1 (1/√3). D) sin^-1(1/2)?.
A transparent solid cylindrical rod has a refractive index of 2/√3 .it is surrounded by air .a light ray is incident at the midpoint of one end of the rod . The incident angle Tita for which the light ray grazes along the wall of the rod is. A) sin^-1 (√3/2) b)sin^-1(2/√3) C) sin^-1 (1/√3). D) sin^-1(1/2)? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A transparent solid cylindrical rod has a refractive index of 2/√3 .it is surrounded by air .a light ray is incident at the midpoint of one end of the rod . The incident angle Tita for which the light ray grazes along the wall of the rod is. A) sin^-1 (√3/2) b)sin^-1(2/√3) C) sin^-1 (1/√3). D) sin^-1(1/2)? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A transparent solid cylindrical rod has a refractive index of 2/√3 .it is surrounded by air .a light ray is incident at the midpoint of one end of the rod . The incident angle Tita for which the light ray grazes along the wall of the rod is. A) sin^-1 (√3/2) b)sin^-1(2/√3) C) sin^-1 (1/√3). D) sin^-1(1/2)?.
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