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Young's double slit experiment is first performed in air and then in a medium other than air. It is found that 8th bright fringe in the medium lies where 5th dark fringe lies in air. The refractive index of the medium is nearly 1)1.59 2)1.69 3)1.78 4)1.25 Explain?
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Young's double slit experiment is first performed in air and then in a...
Explanation:
The position of the bright and dark fringes in Young's double-slit experiment is determined by the wavelength of light and the distance between the slits. When the experiment is performed in a medium other than air, the refractive index of the medium affects the wavelength of light and hence the position of the fringes.
Given:
The 8th bright fringe in the medium lies where the 5th dark fringe lies in air.
Formula:
The distance between the central bright fringe and the nth bright fringe is given by the formula:
d(sinθ) = nλ
where d is the distance between the slits, θ is the angle between the line joining the slit and the bright fringe, n is the order of the bright fringe and λ is the wavelength of light.
Solution:
Let the distance between the slits be d.
In air, the 5th dark fringe lies at a distance of d(sinθ) = 5λ/2 from the central bright fringe.
In the medium, the 8th bright fringe lies at the same distance from the central bright fringe as the 5th dark fringe in air.
Therefore, d(sinθ) = 8λ in the medium.
Dividing the two equations, we get:
sinθ = (8/5)(n_medium/n_air)
where n_medium and n_air are the refractive indices of the medium and air respectively.
Since the angle θ is small, we can use the small-angle approximation sinθ ≈ θ.
Substituting the given values, we get:
(8/5)(n_medium/1) ≈ θ
(8/5)(n_medium) ≈ θ
Substituting this in the formula for d(sinθ), we get:
d((8/5)(n_medium)) = 8λ
d(n_medium) = (5/4)λ
The refractive index of the medium is given by:
n_medium = (5/4)d/λ
Substituting the given values, we get:
n_medium ≈ 1.59
Answer:
Therefore, the refractive index of the medium is approximately 1.59.
The position of the bright and dark fringes in Young's double-slit experiment is determined by the wavelength of light and the distance between the slits. When the experiment is performed in a medium other than air, the refractive index of the medium affects the wavelength of light and hence the position of the fringes.
Given:
The 8th bright fringe in the medium lies where the 5th dark fringe lies in air.
Formula:
The distance between the central bright fringe and the nth bright fringe is given by the formula:
d(sinθ) = nλ
where d is the distance between the slits, θ is the angle between the line joining the slit and the bright fringe, n is the order of the bright fringe and λ is the wavelength of light.
Solution:
Let the distance between the slits be d.
In air, the 5th dark fringe lies at a distance of d(sinθ) = 5λ/2 from the central bright fringe.
In the medium, the 8th bright fringe lies at the same distance from the central bright fringe as the 5th dark fringe in air.
Therefore, d(sinθ) = 8λ in the medium.
Dividing the two equations, we get:
sinθ = (8/5)(n_medium/n_air)
where n_medium and n_air are the refractive indices of the medium and air respectively.
Since the angle θ is small, we can use the small-angle approximation sinθ ≈ θ.
Substituting the given values, we get:
(8/5)(n_medium/1) ≈ θ
(8/5)(n_medium) ≈ θ
Substituting this in the formula for d(sinθ), we get:
d((8/5)(n_medium)) = 8λ
d(n_medium) = (5/4)λ
The refractive index of the medium is given by:
n_medium = (5/4)d/λ
Substituting the given values, we get:
n_medium ≈ 1.59
Answer:
Therefore, the refractive index of the medium is approximately 1.59.
Community Answer
Young's double slit experiment is first performed in air and then in a...
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Young's double slit experiment is first performed in air and then in a medium other than air. It is found that 8th bright fringe in the medium lies where 5th dark fringe lies in air. The refractive index of the medium is nearly 1)1.59 2)1.69 3)1.78 4)1.25 Explain?
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Young's double slit experiment is first performed in air and then in a medium other than air. It is found that 8th bright fringe in the medium lies where 5th dark fringe lies in air. The refractive index of the medium is nearly 1)1.59 2)1.69 3)1.78 4)1.25 Explain? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Young's double slit experiment is first performed in air and then in a medium other than air. It is found that 8th bright fringe in the medium lies where 5th dark fringe lies in air. The refractive index of the medium is nearly 1)1.59 2)1.69 3)1.78 4)1.25 Explain? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Young's double slit experiment is first performed in air and then in a medium other than air. It is found that 8th bright fringe in the medium lies where 5th dark fringe lies in air. The refractive index of the medium is nearly 1)1.59 2)1.69 3)1.78 4)1.25 Explain?.
Young's double slit experiment is first performed in air and then in a medium other than air. It is found that 8th bright fringe in the medium lies where 5th dark fringe lies in air. The refractive index of the medium is nearly 1)1.59 2)1.69 3)1.78 4)1.25 Explain? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Young's double slit experiment is first performed in air and then in a medium other than air. It is found that 8th bright fringe in the medium lies where 5th dark fringe lies in air. The refractive index of the medium is nearly 1)1.59 2)1.69 3)1.78 4)1.25 Explain? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Young's double slit experiment is first performed in air and then in a medium other than air. It is found that 8th bright fringe in the medium lies where 5th dark fringe lies in air. The refractive index of the medium is nearly 1)1.59 2)1.69 3)1.78 4)1.25 Explain?.
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