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If the distance between the slits in a double-slit experiment is halved, what ha

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Question: If the distance between the slits in a double-slit experiment is halved, what happens to the angular position of the first-order maximum? (2023)

Options:

  1. It doubles
  2. It halves
  3. It remains the same
  4. It quadruples

Correct Answer: It doubles

Exam Year: 2023

Solution: 

If the slit separation d is halved, the angle θ for the first-order maximum (d sin θ = λ) will increase, effectively doubling the angle.

If the distance between the slits in a double-slit experiment is halved, what ha

Practice Questions

Q1
If the distance between the slits in a double-slit experiment is halved, what happens to the angular position of the first-order maximum? (2023)
  1. It doubles
  2. It halves
  3. It remains the same
  4. It quadruples

Questions & Step-by-Step Solutions

If the distance between the slits in a double-slit experiment is halved, what happens to the angular position of the first-order maximum? (2023)
  • Step 1: Understand the double-slit experiment. It involves light passing through two slits and creating a pattern of bright and dark spots on a screen.
  • Step 2: Know that the position of these bright spots (maxima) is determined by the formula d sin θ = nλ, where d is the distance between the slits, θ is the angle to the maximum, n is the order of the maximum (1 for first-order), and λ is the wavelength of the light.
  • Step 3: If the distance between the slits (d) is halved, we can write this as d' = d/2.
  • Step 4: Substitute d' into the formula: (d/2) sin θ' = nλ, where θ' is the new angle for the first-order maximum.
  • Step 5: Rearranging gives us sin θ' = (2nλ)/d. Since n is 1 for the first-order maximum, we have sin θ' = (2λ)/d.
  • Step 6: Compare this with the original equation for the first-order maximum: sin θ = (λ)/d. Notice that sin θ' = 2 * sin θ.
  • Step 7: Since sin θ' is double sin θ, the angle θ' must increase, effectively doubling the angle for the first-order maximum.
  • Double-Slit Experiment – The double-slit experiment demonstrates the wave nature of light and how interference patterns are formed based on slit separation and wavelength.
  • Interference Patterns – The angular position of maxima in interference patterns is determined by the relationship between slit separation, wavelength, and angle.
  • First-Order Maximum – The first-order maximum is the first bright fringe observed on either side of the central maximum in an interference pattern.
  • Trigonometric Relationships – Understanding the relationship between slit separation, angle, and wavelength using the equation d sin θ = nλ.
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