Fringe spacing in diffraction patterns

Steps:

• Original double-slit fringe spacing: β = λD/d = 4 mm, where d is slit separation.
• New setup: single slit with width a = d/2; screen distance D' = 2D.
• Single-slit diffraction fringe spacing ≈ λD'/a.
• Substitute: β' = λ(2D)/(d/2) = 4(λD/d) = 4 × 4 mm = 16 mm.

Why D is correct:

• Formula β = λD/d (or a for single slit) shows spacing scales with D and inversely with slit dimension; doubling D and halving effective spacing quadruples β.

Why the others are wrong:

• A: Halving slit dimension alone would double spacing, but doubling D adds another factor of 2.
• B: Ignores both changes, which multiply spacing by 4.
• C: Accounts for doubled D (×2) but misses halved spacing (another ×2).

Final answer: D