Path difference for dark fringes in double-slit interference

Steps:

• Calculate wavelength λ using fringe spacing β = λL/d: λ = βd/L = (8.0×10^{-3} m)(0.10×10^{-3} m)/(2.0 m) = 4.0×10^{-7} m.
• For dark fringes, path difference δ = (m + 1/2)λ, where m = 0,1,2,... for successive orders.
• Second-order dark fringe corresponds to m=1, so δ = (1 + 1/2)λ = (3/2)λ.
• Substitute λ: δ = (3/2)(4.0×10^{-7} m) = 6.0×10^{-7} m.

Why C is correct:

• Matches δ = (3/2)λ for the second dark fringe, per destructive interference condition.

Why the others are wrong:

• A: Equals λ/2, path difference for first-order dark fringe.
• B: Equals λ, path difference for first-order bright fringe.
• D: Equals 2λ, path difference for second-order bright fringe.

Final answer: C