Fringe separation formula in double-slit interference

Steps:

• Fringe separation β = λD / d, where λ is wavelength, D is screen distance, d is slit separation.
• For same β and d, λD is constant.
• Yellow light: λ_y = 600 nm, D_y = 1.0 m, so λ_y D_y = 600 × 1.0.
• Blue light: λ_b = 400 nm, D_b = (600 / 400) × 1.0 = 1.5 m.

Why D is correct:

• D = 1.5 m satisfies λD = constant, as β ∝ λD from the interference formula.

Why the others are wrong:

• A: 0.3 m gives smaller D, increasing β for shorter λ, unlike required same β.
• B: 0.7 m underestimates ratio 600/400 = 1.5, yielding larger β.
• C: 0.75 m approximates but ignores exact 1.5 ratio, resulting in slightly larger β.

Final answer: D