Assertion (A) : Interference pattern is made by using blue light instead of red light, the fringes becomes narrower.
Reason (R ) : In Young's double slit experiment, fringe width is given by the relation `beta = (lambda D)/(d)`

Options

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

Explanation

To solve the question, we need to analyze the assertion and reason provided.

### Step 1: Understand the Assertion
The assertion states that when using blue light instead of red light in an interference pattern, the fringes become narrower.

### Step 2: Understand the Reason
The reason provided explains the relationship between fringe width (β), wavelength (λ), distance from the slits to the screen (D), and the distance between the slits (d). The formula given is:
\[ \beta = \frac{\lambda D}{d} \]
This indicates that fringe width (β) is directly proportional to the wavelength (λ).

### Step 3: Compare Wavelengths
We know that the wavelength of red light (approximately 700 nm) is greater than that of blue light (approximately 450 nm). Thus, we can conclude:
\[ \lambda_{\text{red}} > \lambda_{\text{blue}} \]

### Step 4: Analyze Fringe Width
From the formula for fringe width:
- If we use red light, the fringe width is:
\[ \beta_{\text{red}} = \frac{\lambda_{\text{red}} D}{d} \]
- If we use blue light, the fringe width is:
\[ \beta_{\text{blue}} = \frac{\lambda_{\text{blue}} D}{d} \]

### Step 5: Conclusion on Fringe Width
Since \(\lambda_{\text{red}} > \lambda_{\text{blue}}\), it follows that:
\[ \beta_{\text{red}} > \beta_{\text{blue}} \]
This means that the fringes produced by red light are wider than those produced by blue light.

### Step 6: Final Evaluation
Thus, the assertion is true (the fringes become narrower with blue light), and the reason correctly explains why this is the case. Therefore, both the assertion and reason are true, and the reason is the correct explanation for the assertion.

### Final Answer
Both the assertion and reason are true, and the reason is the correct explanation for the assertion.

---