JEE Physics 2025 Question with Solution

Given: Assertion says that in Young’s double slit experiment, fringes produced by red light are closer than those produced by blue light. Reason says that fringe width is directly proportional to wavelength.

Find: Which option correctly describes the truth of Assertion (A) and Reason (R).

The fringe width in Young’s double slit experiment is given by

$$\beta = \frac{\lambda D}{d}$$

where $\lambda$ is the wavelength of light, $D$ is the distance between slits and screen, and $d$ is the slit separation.

From the formula,

$$\beta \propto \lambda$$

So, a larger wavelength produces a larger fringe width.

Red light has greater wavelength than blue light, so red light produces wider fringes, not closer fringes.

Therefore, Assertion (A) is false.

The Reason (R) states that fringe width is directly proportional to wavelength, which is true.

Therefore, the correct option is B.

Given:

• Assertion (A): red light produces fringes closer than blue light.
• Reason (R): fringe width is directly proportional to wavelength.

Find: Decide the correct option.

Step 1: Use the fringe width relation:

$$\beta = \frac{\lambda D}{d}$$

Step 2: Compare dependence on wavelength:

$$\beta \propto \lambda$$

Thus, fringe width increases when wavelength increases.

Step 3: Compare red and blue light. Since wavelength of red light is greater than wavelength of blue light,

$$\lambda_r > \lambda_b$$

Hence,

$$\beta_r > \beta_b$$

So, fringes due to red light are wider apart, not closer.

Step 4: Judge the statements.

• Assertion (A) is false.
• Reason (R) is true.

Therefore, the correct option is B.