A: The law of conservation of energy is violated during interference.
R: For sustained interference the phase difference between the two waves must charge with time.

Options

A. IF both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark(2)
C. IF Assertion is true statement but Reason is false then mark(3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the question, we need to evaluate both the assertion (A) and the reason (R) provided in the question.

### Step 1: Analyze the Assertion (A)
The assertion states: "The law of conservation of energy is violated during interference."

- The law of conservation of energy states that energy cannot be created or destroyed, only transformed or redistributed.
- In the context of interference, when two waves overlap, they can create regions of constructive interference (bright fringes) and destructive interference (dark fringes).
- The total energy remains constant; it is simply redistributed between the bright and dark fringes.

**Conclusion for Assertion (A):** This statement is **false** because the law of conservation of energy is not violated; energy is conserved and redistributed.

### Step 2: Analyze the Reason (R)
The reason states: "For sustained interference, the phase difference between the two waves must change with time."

- For sustained interference to occur, the two waves must be coherent. Coherent sources maintain a constant phase difference over time.
- If the phase difference were to change, it would lead to a loss of coherence, and thus, sustained interference would not be possible.

**Conclusion for Reason (R):** This statement is also **false** because coherent sources must maintain a constant phase difference for sustained interference.

### Final Conclusion
Both the assertion (A) and the reason (R) are false. Therefore, the correct answer is that both statements are incorrect.

### Summary of the Solution
1. The assertion about the violation of the law of conservation of energy during interference is false; energy is conserved and redistributed.
2. The reason regarding the phase difference needing to change for sustained interference is also false; coherent sources maintain a constant phase difference.