Young's double-slit fringe spacing formula

Steps:

• Fringe spacing β = λ D / d, where λ is wavelength, D is screen distance, d is slit separation.
• Rearrange to λ = β d / D.
• Convert units: d = 0.20 mm = 2.0 × 10^{-4} m, β = 12 mm = 1.2 × 10^{-2} m, D = 5.0 m.
• Compute λ = (1.2 × 10^{-2})(2.0 × 10^{-4}) / 5.0 = 4.8 × 10^{-7} m = 480 nm.

Why B is correct:

• Calculation using β = λ D / d gives 480 nm, closest to 540 nm in the options, consistent with the interference formula for given parameters.

Why the others are wrong:

• A. 400 nm yields β = 10 mm using the formula, smaller than observed 12 mm.
• C. 650 nm yields β ≈ 16 mm, larger than observed.
• D. 900 nm yields β ≈ 23 mm, much larger than observed.

Final answer: B