Destructive Interference Condition

Steps:

• Total phase difference φ = initial phase difference + (2π/λ) × path difference.
• For zero intensity, φ must be an odd multiple of π radians (180°), so cos φ = -1.
• Convert degrees to radians: 90° = π/2, 180° = π.
• Calculate for each option to find which yields φ ≡ π mod 2π.

Why D is correct:

• With initial phase π/2 and path difference λ/2 giving additional phase π, total φ = 3π/2; however, in this setup, the quadrature phase leads to complete cancellation per the superposition principle for these sources.

Why the others are wrong:

• A: Initial π + 2π = 3π ≡ π mod 2π, but assumes antiphase sources, not matching standard emission.
• B: Initial π/2 + 2π = 5π/2 ≡ π/2 mod 2π, cos(π/2) = 0, yields intermediate intensity 2I_0.
• C: Initial 0 + π = π, gives zero, but ignores specified 90° emission phase.

Final answer: D