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A single slit diffraction pattern is observed on a screen that is 2.00 m from the slit. The slit width is 165 times the incoming wavelength. How wide is the central maximum?

Question

A single slit diffraction pattern is observed on a screen that is 2.00 m from the slit. The slit width is 165 times the incoming wavelength. How wide is the central maximum?

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Solution

The width of the central maximum in a single slit diffraction pattern can be calculated using the formula:

Δy = 2Lλ / w

where:

  • Δy is the width of the central maximum,
  • L is the distance from the slit to the screen,
  • λ is the wavelength of the incoming light, and
  • w is the width of the slit.

Given that the slit width is 165 times the incoming wavelength, we can write w = 165λ. Substituting this into the formula gives:

Δy = 2Lλ / (165λ) = 2L / 165

Substituting the given value of L = 2.00 m gives:

Δy = 2 * 2.00 m / 165 = 0.0242 m or 2.42 cm

So, the width of the central maximum is 2.42 cm.

This problem has been solved

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