Path difference for destructive interference

Steps:

• Central bright fringe occurs where path difference δ = 0.
• Dark fringes result from destructive interference when δ = (2n-1)λ/2 for n = 1, 2, 3, ...
• First dark fringe (n=1): δ = λ/2.
• General nth dark fringe: δ = (n - 1/2)λ.

Why C is correct:

• Matches the standard condition for destructive interference: path difference δ = (2n-1)λ/2 = (n - 1/2)λ, where n counts fringes from center.

Why the others are wrong:

• A: nλ/2 applies to bright fringes in some contexts but not dark; ignores odd multiples.
• B: nλ is for bright fringes (constructive interference).
• D: (n + 1/2)λ shifts numbering incorrectly; first dark would be 1.5λ instead of 0.5λ.

Final answer: C