JEE Physics 2025 Question with Solution

Given: Assertion (A): If Young’s double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer.

Find: Whether Assertion (A) and Reason (R) are true, and whether (R) correctly explains (A).

In Young’s double slit experiment, the fringe width is

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

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

In an optically denser medium, the speed of light decreases while the frequency remains unchanged. Therefore,

$$\lambda = \frac{v}{f}$$

so a decrease in $v$ with constant $f$ makes the wavelength smaller.

Hence, in the denser medium,

$$\lambda' = \frac{\lambda}{n}$$

and the new fringe width becomes

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

Since for an optically denser medium, $n > 1$, we get

$$\beta' < \beta$$

Therefore, the fringes come closer together.

So, Assertion (A) is true. Reason (R) is also true, and it correctly explains why the fringe width decreases.

Therefore, the correct option is A.

Given: Fringe spacing in Young’s double slit experiment depends on wavelength.

Find: Whether the reason explains the assertion.

Use the relation

$$\beta \propto \lambda$$

In a denser medium, the speed of light decreases but frequency remains constant, so from

$$\lambda = \frac{v}{f}$$

the wavelength decreases.

Since fringe width is directly proportional to wavelength, the fringes come closer.

Thus both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A). The correct option is A.