Fringe spacing proportional to wavelength

Steps:

• Fringe spacing β = λD/d, where D and d are fixed.
• Thus, β ∝ λ, so new β = old β × (λ_blue / λ_red).
• λ_blue / λ_red = 5.0 × 10^{-7} / 7.0 × 10^{-7} = 5/7 ≈ 0.714.
• β_blue = 3.5 mm × (5/7) = 2.5 mm.

Why A is correct:

• 2.5 mm exactly matches β ∝ λ from double-slit formula.

Why the others are wrong:

• B: Assumes spacing independent of wavelength, but β scales with λ.
• C: Gives larger spacing, opposite to shorter blue wavelength.
• D: Ignores ratio; 5.0 mm exceeds original despite smaller λ.

Final answer: A