Superposition, Coherence & Intensity question from MHT CET 2026 (17 Apr, Shift 1)

Answer: (a)

1. Amplitudes $a$ and $2a$, so intensities $I_0$ and $4I_0$; $I_m = (a + 2a)^2 \propto 9I_0$.
2. $I = I_0 + 4I_0 + 2\sqrt{4}I_0\cos\phi = 5I_0 + 4I_0\cos\phi$
3. Using $\cos\phi = 2\cos^2\dfrac{\phi}{2} - 1$: $I = I_0\left(1 + 8\cos^2\dfrac{\phi}{2}\right)$.
4. With $I_0 = I_m/9$: $I = \dfrac{I_m}{9}\left(1 + 8\cos^2\dfrac{\phi}{2}\right)$. So the answer is (a).