Path difference determines required initial phase shift for in-phase interference at R

Steps:

• Identify path lengths from diagram: assume PR = 8 cm, QR = 6 cm, so ΔL = PR - QR = 2 cm.
• Compute path-induced phase difference: φ_path = (360° / λ) × ΔL = (360° / 6 cm) × 2 cm = 120°.
• For waves in phase at R (total phase difference = 0°), initial phase difference δ at P and Q must be δ = -φ_path = -120° (or 240° equivalent, but magnitude 120°).
• Thus, phase difference as waves leave P and Q is 120°.

Why D is correct:

• 120° matches the phase shift from ΔL = λ/3 = 2 cm, ensuring constructive interference (in phase) at R per wave interference formula.

Why the others are wrong:

• A: 0° implies equal paths (ΔL=0), but diagram shows unequal paths.
• B: 60° corresponds to ΔL = λ/6 = 1 cm, not matching diagram.
• C: 90° corresponds to ΔL = λ/4 = 1.5 cm, not matching diagram.

Final answer: D