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The maximum number of intensity minimum that can be observed in the Fraunhofer diffraction pattern of a single slit (width = 10 µm) illuminated by a laser beam (wavelength 0.630 µm) will be a. 4 b. 7 c. 12 d. 15?
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The maximum number of intensity minimum that can be observed in the Fr...
Calculation of the Number of Intensity Minima:
To determine the maximum number of intensity minima in the Fraunhofer diffraction pattern of a single slit, we can use the formula:
n = (2w/λ) * sin(θ)
where:
n is the number of intensity minima,
w is the width of the slit,
λ is the wavelength of the light,
θ is the angle between the central maximum and the first minimum.
Given:
Width of the slit, w = 10 µm = 10 × 10^(-6) m
Wavelength of the light, λ = 0.630 µm = 0.630 × 10^(-6) m
Calculation:
The angle θ can be approximated using the small angle approximation:
θ ≈ sin(θ) ≈ tan(θ) ≈ y/L
where:
y is the distance of the intensity minima from the central maximum,
L is the distance between the slit and the screen.
Since we are interested in the maximum number of intensity minima, we need to find the smallest angle θ. This occurs when y is at its maximum value, which is half the width of the central maximum.
y = w/2
Substituting the values:
θ = y/L = (w/2)/L = (10 × 10^(-6)/2)/L = 5 × 10^(-6)/L
Using the formula for n:
n = (2w/λ) * sin(θ) = (2 × 10 × 10^(-6) / 0.630 × 10^(-6)) * (5 × 10^(-6)/L)
Simplifying:
n = 2 * (5/0.63) * (10/10^6) * (10^6/L) = 15.87/L
Since n is an integer, the maximum number of intensity minima will be obtained when L is a multiple of 15.87. The smallest value of L that satisfies this condition is L = 15.87 m.
Therefore, the maximum number of intensity minima that can be observed in the Fraunhofer diffraction pattern of a single slit is 15.
Answer:
The correct option is d. 15.
To determine the maximum number of intensity minima in the Fraunhofer diffraction pattern of a single slit, we can use the formula:
n = (2w/λ) * sin(θ)
where:
n is the number of intensity minima,
w is the width of the slit,
λ is the wavelength of the light,
θ is the angle between the central maximum and the first minimum.
Given:
Width of the slit, w = 10 µm = 10 × 10^(-6) m
Wavelength of the light, λ = 0.630 µm = 0.630 × 10^(-6) m
Calculation:
The angle θ can be approximated using the small angle approximation:
θ ≈ sin(θ) ≈ tan(θ) ≈ y/L
where:
y is the distance of the intensity minima from the central maximum,
L is the distance between the slit and the screen.
Since we are interested in the maximum number of intensity minima, we need to find the smallest angle θ. This occurs when y is at its maximum value, which is half the width of the central maximum.
y = w/2
Substituting the values:
θ = y/L = (w/2)/L = (10 × 10^(-6)/2)/L = 5 × 10^(-6)/L
Using the formula for n:
n = (2w/λ) * sin(θ) = (2 × 10 × 10^(-6) / 0.630 × 10^(-6)) * (5 × 10^(-6)/L)
Simplifying:
n = 2 * (5/0.63) * (10/10^6) * (10^6/L) = 15.87/L
Since n is an integer, the maximum number of intensity minima will be obtained when L is a multiple of 15.87. The smallest value of L that satisfies this condition is L = 15.87 m.
Therefore, the maximum number of intensity minima that can be observed in the Fraunhofer diffraction pattern of a single slit is 15.
Answer:
The correct option is d. 15.
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The maximum number of intensity minimum that can be observed in the Fraunhofer diffraction pattern of a single slit (width = 10 µm) illuminated by a laser beam (wavelength 0.630 µm) will be a. 4 b. 7 c. 12 d. 15?
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The maximum number of intensity minimum that can be observed in the Fraunhofer diffraction pattern of a single slit (width = 10 µm) illuminated by a laser beam (wavelength 0.630 µm) will be a. 4 b. 7 c. 12 d. 15? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The maximum number of intensity minimum that can be observed in the Fraunhofer diffraction pattern of a single slit (width = 10 µm) illuminated by a laser beam (wavelength 0.630 µm) will be a. 4 b. 7 c. 12 d. 15? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum number of intensity minimum that can be observed in the Fraunhofer diffraction pattern of a single slit (width = 10 µm) illuminated by a laser beam (wavelength 0.630 µm) will be a. 4 b. 7 c. 12 d. 15?.
The maximum number of intensity minimum that can be observed in the Fraunhofer diffraction pattern of a single slit (width = 10 µm) illuminated by a laser beam (wavelength 0.630 µm) will be a. 4 b. 7 c. 12 d. 15? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The maximum number of intensity minimum that can be observed in the Fraunhofer diffraction pattern of a single slit (width = 10 µm) illuminated by a laser beam (wavelength 0.630 µm) will be a. 4 b. 7 c. 12 d. 15? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum number of intensity minimum that can be observed in the Fraunhofer diffraction pattern of a single slit (width = 10 µm) illuminated by a laser beam (wavelength 0.630 µm) will be a. 4 b. 7 c. 12 d. 15?.
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