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In a single-slit diffraction pattern, what is the angular width of the central m

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Question: In a single-slit diffraction pattern, what is the angular width of the central maximum if the slit width is 0.5 mm and light of wavelength 500 nm is used?

Options:

  1. 0.1 rad
  2. 0.2 rad
  3. 0.3 rad
  4. 0.4 rad

Correct Answer: 0.2 rad

Solution: 

Angular width = 2λ/a = 2(500 nm)/(0.5 mm) = 2(500 x 10^-9)/(0.5 x 10^-3) = 0.002 rad.

In a single-slit diffraction pattern, what is the angular width of the central m

Practice Questions

Q1
In a single-slit diffraction pattern, what is the angular width of the central maximum if the slit width is 0.5 mm and light of wavelength 500 nm is used?
  1. 0.1 rad
  2. 0.2 rad
  3. 0.3 rad
  4. 0.4 rad

Questions & Step-by-Step Solutions

In a single-slit diffraction pattern, what is the angular width of the central maximum if the slit width is 0.5 mm and light of wavelength 500 nm is used?
  • Step 1: Identify the given values. The slit width (a) is 0.5 mm and the wavelength (λ) is 500 nm.
  • Step 2: Convert the units to be consistent. Convert 0.5 mm to meters: 0.5 mm = 0.5 x 10^-3 m.
  • Step 3: Convert 500 nm to meters: 500 nm = 500 x 10^-9 m.
  • Step 4: Use the formula for angular width of the central maximum in a single-slit diffraction pattern: Angular width = 2λ/a.
  • Step 5: Substitute the values into the formula: Angular width = 2(500 x 10^-9 m) / (0.5 x 10^-3 m).
  • Step 6: Calculate the result: Angular width = 2(500 x 10^-9) / (0.5 x 10^-3) = 0.002 rad.
  • Single-Slit Diffraction – The phenomenon where light spreads out after passing through a narrow slit, creating a pattern of light and dark bands.
  • Angular Width Calculation – The formula for calculating the angular width of the central maximum in a diffraction pattern, which is given by 2λ/a, where λ is the wavelength and a is the slit width.
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