Phase difference shifts interference conditions

Steps:

• Identify initial phase difference of 180° (π radians) between sources P and Q.
• For destructive interference (minimum) at S, total phase difference must be odd multiple of π: (2n+1)π.
• Total phase = (2π/λ)(PS - QS) + π = (2n+1)π.
• Solve: (2π/λ)Δx = 2nπ, so Δx = nλ.

Why A is correct:

• With 180° source phase difference, path difference of nλ produces destructive interference, per phase condition formula.

Why the others are wrong:

• B: Applies to minima without initial phase shift.
• C: Equivalent to (n+1)λ, which is for maxima without phase shift.
• D: Incorrect multiple; doesn't match solved equation.

Final answer: A