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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.
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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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