Destructive Interference Condition Steps:

• Zero intensity requires destructive interference, where waves arrive with phase difference of (2n+1)π radians.
• Phase difference from path is (2π/λ) × Δpath; for n=0, Δpath = λ/2 gives π radians.
• If sources emit in phase, initial phase difference is 0, so Δpath = λ/2 yields total π for destructive interference.
• Other initial phases or path differences alter total phase, preventing exact destructive interference.

Why D is correct:

• Sources in phase mean initial phase difference of 0; path difference λ/2 adds π radians, satisfying the condition for destructive interference per wave superposition.

Why the others are wrong:

• A: 180° (π radians) initial plus λ/2 path (π radians) totals 2π, causing constructive interference.
• B: Sources in phase with path difference λ adds 2π radians, resulting in constructive interference.
• C: 90° (π/2 radians) initial plus λ path (2π radians) totals 5π/2 ≡ π/2 mod 2π, yielding partial interference, not zero intensity.

Final answer: D