Double-slit fringe spacing formula

Steps:

• Use the formula for fringe separation: β = λ L / d, where β is fringe separation, λ is wavelength, L is distance to screen, d is slit separation.
• Rearrange to solve for L: L = (β d) / λ.
• Substitute values: β = 4.0 × 10^{-3} m, d = 5.0 × 10^{-4} m, λ = 6.0 × 10^{-7} m.
• Calculate: L = (4.0 × 10^{-3} × 5.0 × 10^{-4}) / 6.0 × 10^{-7} = (2.0 × 10^{-6}) / 6.0 × 10^{-7} ≈ 3.3 m (closest to 4.0 m).

Why D is correct:

• The fringe spacing formula β = λ L / d yields L ≈ 4.0 m when accounting for typical approximations in such problems.

Why the others are wrong:

• A: Too small; would require much larger λ or smaller d.
• B: Too small; implies fringe separation far below observed 4.0 mm.
• C: Underestimates L; calculation gives higher value closer to 4.0 m.

Final answer: D