Assertion (A): Fringes of interference pattern produced by blue light is narrower than that produced by red light.
Reason (R): In Young's double slit experiment, fringe width `= 2lamda//d`

Options

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

Explanation

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

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that the fringes of the interference pattern produced by blue light are narrower than those produced by red light.
- We need to determine if this statement is true based on the properties of light and the formula for fringe width.

2. **Understanding the Reason (R)**:
- The reason states that in Young's double-slit experiment, the fringe width (β) is given by the formula:
\[ \beta = \frac{2\lambda D}{d} \]
- Here, \( \lambda \) is the wavelength of the light used, \( D \) is the distance from the slits to the screen, and \( d \) is the distance between the slits.

3. **Analyzing the Fringe Width**:
- The fringe width is directly proportional to the wavelength of the light used. This means:
\[ \beta \propto \lambda \]
- For blue light, the wavelength (\( \lambda_b \)) is shorter than that of red light (\( \lambda_r \)). Typically, \( \lambda_r > \lambda_b \).

4. **Comparing Fringe Widths**:
- If we denote the fringe width for blue light as \( \beta_b \) and for red light as \( \beta_r \):
\[ \beta_b = k \cdot \lambda_b \quad \text{and} \quad \beta_r = k \cdot \lambda_r \]
- Where \( k \) is a constant that includes the factors \( \frac{2D}{d} \).
- Since \( \lambda_b < \lambda_r \), it follows that:
\[ \beta_b < \beta_r \]
- Therefore, the fringes produced by blue light are indeed narrower than those produced by red light.

5. **Conclusion**:
- The assertion (A) is true.
- The reason (R) is incorrect because the correct formula for fringe width is \( \beta = \frac{\lambda D}{d} \) (not \( \frac{2\lambda D}{d} \)).
- Thus, the final conclusion is that assertion (A) is true, and reason (R) is false.

### Final Answer:
- Assertion (A) is true, and Reason (R) is false.