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.