QJEEM25Ph827f: JEE Main 2025 Physics - Class 12 JEEM25Ph827f Solution: Given below are two statements : one is labelled as Assertion…

First, let us restate the statements:

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

Reason (R): The speed of light reduces in an optically denser medium than air while its frequency does not change.

1. Analysis of the Assertion (A)

When the experiment is performed in a denser medium:

The speed of light in the medium is $v = \frac{c}{n}$ , where $n$ is the refractive index ( n > 1 for a denser medium).

The frequency $f$ of light remains the same when light enters a different medium, but its wavelength $\lambda$ changes according to:

$\lambda_{\text{medium}} = \frac{v}{f} = \frac{c}{nf}.$

Hence $\lambda_{\text{medium}} = \frac{\lambda_{\text{vacuum}}}{n}$ .

In a Young’s double slit experiment, the fringe spacing $\beta$ is given by

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

where

$D$ is the distance from the slits to the screen,

$d$ is the slit separation, and

$\lambda$ is the wavelength in the medium where the pattern forms.

Since $\lambda$ decreases in a denser medium ( \lambda_{\text{medium}} < \lambda_{\text{air}} ), the fringe spacing $\beta$ also decreases, causing the fringes to come closer together. Thus, Assertion (A) is true.

2. Analysis of the Reason (R)

The reason states that the speed of light decreases in a denser medium ( v < c ) but the frequency remains the same. This is a well-known principle from wave theory: on crossing the boundary between two media, the frequency of the wave is invariant, while the speed and hence the wavelength change.

Because $\lambda = \frac{v}{f}$ and $v$ decreases but $f$ remains unchanged, $\lambda$ must decrease. This phenomenon is precisely why the fringes get closer in the experiment described in (A). Hence, Reason (R) is true.

3. Does (R) correctly explain (A)?

Yes. The fringes come closer because the wavelength becomes smaller in the denser medium, and that directly follows from the fact that the speed decreases while frequency remains the same (Reason (R)).

Therefore, both (A) and (R) are true, and (R) is the correct explanation of (A).

Conclusion

Among the given options, the correct choice is:

(C) Both (A) and (R) are true and (R) is the correct explanation of (A).