In-phase interference: intensity proportional to square of summed amplitudes

Steps:

• Original: amplitudes A (P) + A (Q) = 2A resultant; I ∝ (2A)^2 = 4A².
• New: P amplitude doubled to 2A, Q remains A; resultant = 3A.
• New intensity I' ∝ (3A)^2 = 9A².
• I'/I = 9A²/4A² = 9/4 = 2.25.

Why C is correct:

• Formula for coherent in-phase superposition gives I' = (A_P + A_Q)^2 proportional intensity, so (2A + A)^2/(A + A)^2 I = 9/4 I ≈ 2.3I.

Why the others are wrong:

• A: Assumes destructive interference, yielding (2A - A)^2/(2A)^2 I = 1/4 I = 0.25I, close to 0.4I.
• B: Assumes incoherent addition, I_p' + I_q = 4I_single + I_single = 5I_single, but original I = 4I_single so 5/4 I = 1.25I, near 1.5I.
• D: Mistakenly adds intensities linearly after doubling, ignoring phase, yielding ~3I.

Final answer: C