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The maximum number of intensity minima 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
Correct answer is option 'D'. Can you explain this answer?
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The number of intensity minima in the Fraunhofer diffraction pattern of a single slit is given by the formula:

N = (2W/λ)sinθ

Where W is the width of the slit, λ is the wavelength of the light, and θ is the angle between the direction of the incident light and the direction of the diffracted light.

For a single slit with a width of 10 μm and a wavelength of 500 nm (corresponding to green light), the maximum number of intensity minima can be calculated as follows:

N = (2 × 10 μm / 500 nm)sinθ

The sine function has a maximum value of 1, so the maximum number of intensity minima occurs when sinθ = 1. Therefore:

N = (2 × 10 μm / 500 nm) × 1
N = 80

Therefore, the maximum number of intensity minima that can be observed in the Fraunhofer diffraction pattern of a single slit with a width of 10 μm and a wavelength of 500 nm is 80.
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