A : If the phase difference between the light waves emerging from the slits of the Young.s experiment is `pi`-raidan, the central fringe will be dark
R : Phase difference is equal to `(2pi"/"lambda)` times the path difference.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of A
C. A is true and R is false
D. Both A and R are false

Answer

To solve the problem step by step, we need to analyze the statements A and R regarding the Young's double slit experiment.

### Step 1: Understand Statement A
**Statement A**: If the phase difference between the light waves emerging from the slits of Young's experiment is π radians, the central fringe will be dark.

- In Young's double slit experiment, the central fringe is typically a bright fringe when the path difference is zero (i.e., when the waves from both slits arrive in phase).
- A phase difference of π radians corresponds to a path difference of λ/2 (since phase difference Δφ = (2π/λ) * Δx).
- When the path difference is λ/2, the waves interfere destructively, resulting in a dark fringe.

**Conclusion for A**: Statement A is true.

### Step 2: Understand Statement R
**Statement R**: Phase difference is equal to (2π/λ) times the path difference.

- This statement is a fundamental principle of wave optics. The phase difference Δφ between two waves is given by the formula:
\[ \Delta \phi = \frac{2\pi}{\lambda} \Delta x \]
- Here, Δx is the path difference between the two waves. This relationship is indeed correct.

**Conclusion for R**: Statement R is also true.

### Step 3: Analyze the Relationship Between A and R
- While both statements A and R are true, we need to determine if R correctly explains A.
- Statement A indicates that a phase difference of π leads to a dark fringe. Statement R provides the relationship between phase difference and path difference but does not specifically explain why a phase difference of π results in a dark fringe at the center.

**Conclusion**: Both A and R are true, but R is not the correct explanation for A.

### Final Answer
Both statements A and R are true, but R is not the correct explanation for A. Therefore, the correct answer is option 2.

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