Match List-I with List-II regarding the interference pattern...

The phase difference $\Delta \phi$ and path difference $\Delta x$ are related by $\Delta \phi = \dfrac{2\pi}{\lambda} \Delta x$.

For (A): $\Delta x = 0$ corresponds to a phase difference of zero, which is the condition for the central maximum. Hence, (A) matches with (II).

For (B): $\Delta x = \dfrac{\lambda}{2}$ corresponds to $\Delta \phi = \pi$. This satisfies the condition for the first minimum, $\Delta \phi = (2n-1)\pi$ with $n=1$. Hence, (B) matches with (I).

For (C): $\Delta \phi = 2\pi$ satisfies the condition for constructive interference $\Delta \phi = 2n\pi$ with $n=1$, which is the first maximum. Hence, (C) matches with (IV).

For (D): $\Delta \phi = 5\pi$ satisfies the condition for destructive interference $\Delta \phi = (2n-1)\pi$ with $n=3$, which is the third minimum. Hence, (D) matches with (III).

The correct matching is (A)-(II), (B)-(I), (C)-(IV), (D)-(III).

Answer: (A)-(II), (B)-(I), (C)-(IV), (D)-(III)