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In Young's double-slit experiment, if the distance between the slits is doubled

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Question: In Young\'s double-slit experiment, if the distance between the slits is doubled while keeping the wavelength constant, what happens to the fringe width?

Options:

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

Correct Answer: It halves

Solution: 

Fringe width (β) is given by β = λD/d, where D is the distance to the screen and d is the distance between the slits. If d is doubled, β halves.

In Young's double-slit experiment, if the distance between the slits is doubled

Practice Questions

Q1
In Young's double-slit experiment, if the distance between the slits is doubled while keeping the wavelength constant, what happens to the fringe width?
  1. It doubles
  2. It halves
  3. It remains the same
  4. It quadruples

Questions & Step-by-Step Solutions

In Young's double-slit experiment, if the distance between the slits is doubled while keeping the wavelength constant, what happens to the fringe width?
  • Step 1: Understand the formula for fringe width, which is β = λD/d.
  • Step 2: Identify the variables in the formula: λ is the wavelength, D is the distance to the screen, and d is the distance between the slits.
  • Step 3: Note that in this scenario, the wavelength (λ) and the distance to the screen (D) remain constant.
  • Step 4: Recognize that if the distance between the slits (d) is doubled, we replace d with 2d in the formula.
  • Step 5: Substitute into the formula: β = λD/(2d).
  • Step 6: Compare the new fringe width (β) with the original fringe width (β = λD/d).
  • Step 7: Since β = λD/(2d) is half of β = λD/d, we conclude that the new fringe width is half of the original fringe width.
  • Fringe Width in Interference Patterns – Understanding how the fringe width in Young's double-slit experiment is affected by changes in slit separation and wavelength.
  • Relationship Between Variables – Applying the formula β = λD/d to analyze how changes in the distance between slits (d) influence the fringe width (β).
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