Young's double-slit fringe separation

Steps:

• Use the formula for fringe separation: Δy = λL / d, so L = Δy × d / λ.
• Convert units: λ = 650 × 10⁻⁹ m = 6.5 × 10⁻⁷ m; d = 0.12 × 10⁻³ m = 1.2 × 10⁻⁴ m; Δy = 7.5 × 10⁻² m.
• Substitute values: L = (7.5 × 10⁻²) × (1.2 × 10⁻⁴) / (6.5 × 10⁻⁷).
• Calculate: numerator = 9 × 10⁻⁶; L = 9 × 10⁻⁶ / 6.5 × 10⁻⁷ ≈ 13.8 m ≈ 14 m.

Why D is correct:

• Matches L ≈ 14 m from the fringe separation formula Δy = λL / d.

Why the others are wrong:

• A: Half of correct value, likely from using mm for d without conversion.
• B: Double of A but still underestimates L by factor of 5.
• C: Underestimates L by factor of 2, perhaps from wavelength error.

Final answer: D