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In a YDSE using light, the apparatus has two slits of unequal widths. When only slit-1 is open, the maximum observed intensity on the screen is 9I0. When only slit-2 is open the maximum observed intensity is 4I0. When the both slits are open, an interference pattern appears on the screen. The ratio o f principle maxima to that of the nearest minima is _________ .
Correct answer is '25'. Can you explain this answer?
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In a YDSE using light, the apparatus has two slits of unequal widths. ...
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In a YDSE using light, the apparatus has two slits of unequal widths. ...
Given information:
- Maximum intensity when only slit-1 is open: 9I0
- Maximum intensity when only slit-2 is open: 4I0
- Interference pattern observed when both slits are open
To find:
The ratio of principal maxima to the nearest minima
Solution:
The intensity of the interference pattern produced by two slits can be calculated using the formula:
I = 4I0cos²(πd sinθ/λ)
Where:
- I is the intensity at a point on the screen
- I0 is the intensity when only one slit is open
- d is the distance between the two slits
- θ is the angle of observation
- λ is the wavelength of light
Step 1: Finding the intensity when both slits are open
Let's assume the widths of slit-1 and slit-2 are a and b respectively.
When only slit-1 is open, the maximum intensity observed is 9I0.
So, I1 = 9I0
When only slit-2 is open, the maximum intensity observed is 4I0.
So, I2 = 4I0
Using the formula, we can write:
I = 4I0cos²(πd sinθ/λ)
For the principal maxima, cos²(πd sinθ/λ) = 1.
So, the intensity at the principal maxima is:
I_max = 4I0
Step 2: Finding the intensity at the nearest minima
For the nearest minima, cos²(πd sinθ/λ) = 0.
So, the intensity at the nearest minima is:
I_min = 0
Step 3: Calculating the ratio
The ratio of principal maxima to the nearest minima is given by:
Ratio = I_max / I_min
Since I_min = 0, the ratio is undefined.
However, it is possible that the question intends to ask for the ratio of the intensity at the principal maxima to the average intensity at the nearest minima. In that case, we can calculate the average intensity at the nearest minima by considering the contributions from both slits.
I_min_avg = (I1 + I2) / 2
= (9I0 + 4I0) / 2
= 13I0 / 2
So, the ratio of principal maxima to the average intensity at the nearest minima is:
Ratio = I_max / I_min_avg
= 4I0 / (13I0 / 2)
= 8 / 13
The correct answer is 8/13, not 25. It seems there might be a mistake in the question or the answer key.
- Maximum intensity when only slit-1 is open: 9I0
- Maximum intensity when only slit-2 is open: 4I0
- Interference pattern observed when both slits are open
To find:
The ratio of principal maxima to the nearest minima
Solution:
The intensity of the interference pattern produced by two slits can be calculated using the formula:
I = 4I0cos²(πd sinθ/λ)
Where:
- I is the intensity at a point on the screen
- I0 is the intensity when only one slit is open
- d is the distance between the two slits
- θ is the angle of observation
- λ is the wavelength of light
Step 1: Finding the intensity when both slits are open
Let's assume the widths of slit-1 and slit-2 are a and b respectively.
When only slit-1 is open, the maximum intensity observed is 9I0.
So, I1 = 9I0
When only slit-2 is open, the maximum intensity observed is 4I0.
So, I2 = 4I0
Using the formula, we can write:
I = 4I0cos²(πd sinθ/λ)
For the principal maxima, cos²(πd sinθ/λ) = 1.
So, the intensity at the principal maxima is:
I_max = 4I0
Step 2: Finding the intensity at the nearest minima
For the nearest minima, cos²(πd sinθ/λ) = 0.
So, the intensity at the nearest minima is:
I_min = 0
Step 3: Calculating the ratio
The ratio of principal maxima to the nearest minima is given by:
Ratio = I_max / I_min
Since I_min = 0, the ratio is undefined.
However, it is possible that the question intends to ask for the ratio of the intensity at the principal maxima to the average intensity at the nearest minima. In that case, we can calculate the average intensity at the nearest minima by considering the contributions from both slits.
I_min_avg = (I1 + I2) / 2
= (9I0 + 4I0) / 2
= 13I0 / 2
So, the ratio of principal maxima to the average intensity at the nearest minima is:
Ratio = I_max / I_min_avg
= 4I0 / (13I0 / 2)
= 8 / 13
The correct answer is 8/13, not 25. It seems there might be a mistake in the question or the answer key.
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In a YDSE using light, the apparatus has two slits of unequal widths. When only slit-1 is open, the maximum observed intensity on the screen is 9I0. When only slit-2 is open the maximum observed intensity is 4I0. When the both slits are open, an interference pattern appears on the screen. The ratio o f principle maxima to that of the nearest minima is _________ .Correct answer is '25'. Can you explain this answer?
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In a YDSE using light, the apparatus has two slits of unequal widths. When only slit-1 is open, the maximum observed intensity on the screen is 9I0. When only slit-2 is open the maximum observed intensity is 4I0. When the both slits are open, an interference pattern appears on the screen. The ratio o f principle maxima to that of the nearest minima is _________ .Correct answer is '25'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a YDSE using light, the apparatus has two slits of unequal widths. When only slit-1 is open, the maximum observed intensity on the screen is 9I0. When only slit-2 is open the maximum observed intensity is 4I0. When the both slits are open, an interference pattern appears on the screen. The ratio o f principle maxima to that of the nearest minima is _________ .Correct answer is '25'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a YDSE using light, the apparatus has two slits of unequal widths. When only slit-1 is open, the maximum observed intensity on the screen is 9I0. When only slit-2 is open the maximum observed intensity is 4I0. When the both slits are open, an interference pattern appears on the screen. The ratio o f principle maxima to that of the nearest minima is _________ .Correct answer is '25'. Can you explain this answer?.
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