Question

Given below are two statements, one labeled as Assertion (A) and the other as Reason (R). Assertion (A): In Young’s double slit experiment, the fringes produced by red light are closer compared to those produced by blue light. Reason (R): The fringe width is directly proportional to the wavelength of light. In the light of the above statements, choose the correct answer from the options given below:

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

Hint:

In Young’s double-slit experiment: - Fringe width is given by \( \beta = \frac{\lambda D}{d} \). - Longer wavelengths (e.g., red) produce wider fringes. - Shorter wavelengths (e.g., blue) produce narrower fringes.

Answer 1

The Correct Option is B

Step 1: Understanding the fringe width formula. The fringe width in Young’s double-slit experiment is given by: \[ \beta = \frac{\lambda D}{d}, \] where: - \( \lambda \) is the wavelength of the light, - \( D \) is the distance between slits and screen, - \( d \) is the separation between the slits. Step 2: Analyzing Assertion (A). Since \( \beta \propto \lambda \), red light (\(\lambda\) is larger) produces wider fringes than blue light (\(\lambda\) is smaller). Thus, Assertion (A) is incorrect because it states the opposite. Step 3: Analyzing Reason (R). The fringe width is indeed proportional to the wavelength, which is a correct statement. Since (A) is false but (R) is true, the correct choice is: \[ \boxed{\text{(2) (A) is false, but (R) is true.}} \]

Answer 2

Step 1: Formula for fringe width in Young’s double slit experiment. 
The fringe width is given by: \[ \beta = \frac{\lambda D}{d} \] where \( \lambda \) = wavelength of light, \( D \) = distance between slits and screen, \( d \) = distance between the two slits.

Step 2: Relation between fringe width and wavelength.
From the above formula: \[ \beta \propto \lambda \] i.e., the fringe width is directly proportional to the wavelength.

Step 3: Compare red and blue light.
The wavelength of red light (\( \lambda_r \)) is greater than that of blue light (\( \lambda_b \)): \[ \lambda_r > \lambda_b. \] Hence, the fringes produced by red light are wider apart (not closer) than those produced by blue light.

Step 4: Verify the truth of the statements.
- Assertion (A): False — because red fringes are farther apart, not closer. - Reason (R): True — because fringe width is directly proportional to wavelength.

---

Final Answer:

\[ \boxed{(A)\ \text{is false, but (R) is true.}} \]