Fringe spacing in double-slit interference

Steps:

• Fringe separation formula: x = λD / a, where λ is wavelength.
• Initial: x = λD / a.
• New parameters: D' = D/2, a' = a/2.
• New separation: x' = λ(D/2) / (a/2) = λD / a = x.

Why B is correct:

• Fringe separation β = λD/a depends on the ratio D/a, which remains constant when both D and a are halved.

Why the others are wrong:

• A: x/2 occurs if only D is halved, increasing angular spread but not compensated by a.
• C: 2x occurs if only a is halved, widening fringes without D change.
• D: 4x requires opposite changes, like doubling D and halving a twice.

Final answer: B