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The ratio of the intensity at the centre of a bright fringe to the intensity at a point one quarter of the distance between two successive same fringe from the centre is?a)2 b)1/2 c)4 d)16?
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Explanation:
When monochromatic light passes through a single slit, the diffracted light produces a central bright fringe and a series of alternate dark and bright fringes on either side of the central fringe. The intensity of the light at different points on the screen is given by the equation:
I = I₀ (sinθ/θ)²
Where I₀ is the maximum intensity at the centre of the bright fringe and θ is the angle between the incident beam and the diffracted beam.
Intensity at the centre of the bright fringe:
At the centre of the bright fringe, the angle θ is zero. Therefore, the intensity at the centre of the bright fringe is given by:
I(center) = I₀ (sin 0/0)² = I₀
Intensity at a point one quarter of the distance between two successive same fringe from the centre:
Let d be the distance between two successive same fringes on the screen. Then the distance between the centre and the point one quarter of the distance between two successive same fringe from the centre is d/4. At this point, the angle θ is given by:
sinθ = (d/4)/√((d/2)² + L²)
Where L is the distance between the slit and the screen.
Therefore, the intensity at this point is given by:
I(d/4) = I₀ (sinθ/θ)² = I₀ [(d/4)/√((d/2)² + L²)]²/[(d/4)/√((d/2)² + L²)]²
Simplifying the above equation, we get:
I(d/4) = I₀/4
Therefore, the ratio of the intensity at the centre of the bright fringe to the intensity at a point one quarter of the distance between two successive same fringe from the centre is:
I(center)/I(d/4) = I₀/I₀/4 = 4
Therefore, the correct option is (c) 4.
When monochromatic light passes through a single slit, the diffracted light produces a central bright fringe and a series of alternate dark and bright fringes on either side of the central fringe. The intensity of the light at different points on the screen is given by the equation:
I = I₀ (sinθ/θ)²
Where I₀ is the maximum intensity at the centre of the bright fringe and θ is the angle between the incident beam and the diffracted beam.
Intensity at the centre of the bright fringe:
At the centre of the bright fringe, the angle θ is zero. Therefore, the intensity at the centre of the bright fringe is given by:
I(center) = I₀ (sin 0/0)² = I₀
Intensity at a point one quarter of the distance between two successive same fringe from the centre:
Let d be the distance between two successive same fringes on the screen. Then the distance between the centre and the point one quarter of the distance between two successive same fringe from the centre is d/4. At this point, the angle θ is given by:
sinθ = (d/4)/√((d/2)² + L²)
Where L is the distance between the slit and the screen.
Therefore, the intensity at this point is given by:
I(d/4) = I₀ (sinθ/θ)² = I₀ [(d/4)/√((d/2)² + L²)]²/[(d/4)/√((d/2)² + L²)]²
Simplifying the above equation, we get:
I(d/4) = I₀/4
Therefore, the ratio of the intensity at the centre of the bright fringe to the intensity at a point one quarter of the distance between two successive same fringe from the centre is:
I(center)/I(d/4) = I₀/I₀/4 = 4
Therefore, the correct option is (c) 4.
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The ratio of the intensity at the centre of a bright fringe to the intensity at a point one quarter of the distance between two successive same fringe from the centre is?a)2 b)1/2 c)4 d)16?
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The ratio of the intensity at the centre of a bright fringe to the intensity at a point one quarter of the distance between two successive same fringe from the centre is?a)2 b)1/2 c)4 d)16? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The ratio of the intensity at the centre of a bright fringe to the intensity at a point one quarter of the distance between two successive same fringe from the centre is?a)2 b)1/2 c)4 d)16? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of the intensity at the centre of a bright fringe to the intensity at a point one quarter of the distance between two successive same fringe from the centre is?a)2 b)1/2 c)4 d)16?.
The ratio of the intensity at the centre of a bright fringe to the intensity at a point one quarter of the distance between two successive same fringe from the centre is?a)2 b)1/2 c)4 d)16? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The ratio of the intensity at the centre of a bright fringe to the intensity at a point one quarter of the distance between two successive same fringe from the centre is?a)2 b)1/2 c)4 d)16? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of the intensity at the centre of a bright fringe to the intensity at a point one quarter of the distance between two successive same fringe from the centre is?a)2 b)1/2 c)4 d)16?.
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