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: The formula for fringe width in Young’s double-slit experiment is defined as: \[ \beta = \frac{\lambda D}{d}, \] where \( \lambda \) represents the wavelength of the light, \( D \) is the distance from the slits to the screen, and \( d \) is the separation distance between the slits.

Step 2: For Assertion (A): The fringe width \( \beta \) is directly proportional to the wavelength \( \lambda \) (\( \beta \propto \lambda \)). Consequently, red light, possessing a larger wavelength, generates wider fringes compared to blue light, which has a smaller wavelength. Therefore, Assertion (A) is false as it asserts the inverse. 

Step 3: For Reason (R): The fringe width is, in fact, proportional to the wavelength. This statement is correct. 

Given that Assertion (A) is false and Reason (R) is true, the correct selection is: \[ \boxed{\text{(2) (A) is false, but (R) is true.}} \]