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A plane monochromatic light wave falls normally on a diaphragm with two narrow slits separated by a distance d = 2.5 mm. A fringe pattern is formed on a screen placed at a distance l = 100 cm behind the diaphragm. By what distance in mm will these fringes be displaced when one of the slits is covered by a glass plate of thickness h = 10 μm?
Correct answer is '2'. Can you explain this answer?
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A plane monochromatic light wave falls normally on a diaphragm with t...
Given:
- Distance between the two slits (d) = 2.5 mm
- Distance between the diaphragm and the screen (l) = 100 cm = 1000 mm
- Thickness of the glass plate (h) = 10 μm
To Find:
The distance by which the fringes will be displaced when one of the slits is covered by a glass plate.
Explanation:
When a monochromatic light wave falls normally on a diaphragm with two narrow slits, it creates an interference pattern on the screen placed behind it. This pattern consists of alternating bright and dark fringes. The position of these fringes is determined by the path difference between the two slits.
When one of the slits is covered by a glass plate, the light passing through the uncovered slit travels a distance l and reaches the screen directly. However, the light passing through the covered slit travels a distance l + h (due to the additional thickness of the glass plate) before reaching the screen.
Key Point:
The path difference between the two slits is given by the formula:
Δx = (l + h) - l = h
So, the path difference between the two slits is equal to the thickness of the glass plate.
Key Point:
The position of the fringes is determined by the path difference between the two slits. The distance between consecutive bright or dark fringes is given by the formula:
Δx = λ * l / d
where λ is the wavelength of the light.
Since the distance between consecutive fringes is directly proportional to the wavelength of light, it remains constant for a given setup.
Therefore, the displacement of the fringes caused by the glass plate is equal to the path difference, which is h = 10 μm = 0.01 mm.
Hence, the fringes will be displaced by a distance of 2 mm when one of the slits is covered by the glass plate.
- Distance between the two slits (d) = 2.5 mm
- Distance between the diaphragm and the screen (l) = 100 cm = 1000 mm
- Thickness of the glass plate (h) = 10 μm
To Find:
The distance by which the fringes will be displaced when one of the slits is covered by a glass plate.
Explanation:
When a monochromatic light wave falls normally on a diaphragm with two narrow slits, it creates an interference pattern on the screen placed behind it. This pattern consists of alternating bright and dark fringes. The position of these fringes is determined by the path difference between the two slits.
When one of the slits is covered by a glass plate, the light passing through the uncovered slit travels a distance l and reaches the screen directly. However, the light passing through the covered slit travels a distance l + h (due to the additional thickness of the glass plate) before reaching the screen.
Key Point:
The path difference between the two slits is given by the formula:
Δx = (l + h) - l = h
So, the path difference between the two slits is equal to the thickness of the glass plate.
Key Point:
The position of the fringes is determined by the path difference between the two slits. The distance between consecutive bright or dark fringes is given by the formula:
Δx = λ * l / d
where λ is the wavelength of the light.
Since the distance between consecutive fringes is directly proportional to the wavelength of light, it remains constant for a given setup.
Therefore, the displacement of the fringes caused by the glass plate is equal to the path difference, which is h = 10 μm = 0.01 mm.
Hence, the fringes will be displaced by a distance of 2 mm when one of the slits is covered by the glass plate.
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Community Answer
A plane monochromatic light wave falls normally on a diaphragm with t...
Due to introduction of glass plate, width of fringe does not change.
Here, width of fringe,
According to problem,
D = l = 100 cm = 1m, d = 2.5 mm = 2.5 x 10-3 m
h = 10 x 10-6 m, n = 1.5
∴ 
Putting the values, we get
Δy = 2×10−3
Δy = 2 mm.
In the diagram, upper slit is covered by glass plate.
So, fringe pattern on screen shifts upward.
Remarks : In this case, central bright fringe does not coincide with the centre of secreen.
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A plane monochromatic light wave falls normally on a diaphragm with two narrow slits separated by a distance d = 2.5 mm. A fringe pattern is formed on a screen placed at a distance l = 100 cm behind the diaphragm. By what distance in mm will these fringes be displaced when one of the slits is covered by a glass plate of thickness h = 10 μm?Correct answer is '2'. Can you explain this answer?
Question Description
A plane monochromatic light wave falls normally on a diaphragm with two narrow slits separated by a distance d = 2.5 mm. A fringe pattern is formed on a screen placed at a distance l = 100 cm behind the diaphragm. By what distance in mm will these fringes be displaced when one of the slits is covered by a glass plate of thickness h = 10 μm?Correct answer is '2'. 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 plane monochromatic light wave falls normally on a diaphragm with two narrow slits separated by a distance d = 2.5 mm. A fringe pattern is formed on a screen placed at a distance l = 100 cm behind the diaphragm. By what distance in mm will these fringes be displaced when one of the slits is covered by a glass plate of thickness h = 10 μm?Correct answer is '2'. 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 plane monochromatic light wave falls normally on a diaphragm with two narrow slits separated by a distance d = 2.5 mm. A fringe pattern is formed on a screen placed at a distance l = 100 cm behind the diaphragm. By what distance in mm will these fringes be displaced when one of the slits is covered by a glass plate of thickness h = 10 μm?Correct answer is '2'. Can you explain this answer?.
A plane monochromatic light wave falls normally on a diaphragm with two narrow slits separated by a distance d = 2.5 mm. A fringe pattern is formed on a screen placed at a distance l = 100 cm behind the diaphragm. By what distance in mm will these fringes be displaced when one of the slits is covered by a glass plate of thickness h = 10 μm?Correct answer is '2'. 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 plane monochromatic light wave falls normally on a diaphragm with two narrow slits separated by a distance d = 2.5 mm. A fringe pattern is formed on a screen placed at a distance l = 100 cm behind the diaphragm. By what distance in mm will these fringes be displaced when one of the slits is covered by a glass plate of thickness h = 10 μm?Correct answer is '2'. 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 plane monochromatic light wave falls normally on a diaphragm with two narrow slits separated by a distance d = 2.5 mm. A fringe pattern is formed on a screen placed at a distance l = 100 cm behind the diaphragm. By what distance in mm will these fringes be displaced when one of the slits is covered by a glass plate of thickness h = 10 μm?Correct answer is '2'. Can you explain this answer?.
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