Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason(R).
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.
In the light of the above statements, choose the most appropriate answer from the options given below :

Assertion (A):

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

In Young’s double-slit experiment, the fringe width ($\beta$) is given by:

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

where:

$\lambda$ = wavelength of light in the medium,

$D$ = distance between slits and screen,

$d$ = distance between the slits.

In an optically denser medium, the speed of light decreases, and hence the wavelength of light in the medium becomes smaller ($\lambda_m = \frac{\lambda}{n}$, where $n$ is the refractive index). As a result, the fringe width $\beta$ decreases, causing the fringes to come closer.

Thus, Assertion (A) is correct.

Reason (R):

"The speed of light reduces in an optically denser medium than air while its frequency does not change."

In a denser medium, the speed of light decreases due to the material's refractive index ($v = \frac{c}{n}$). However, the frequency of light remains constant because frequency is determined by the source of the light, not the medium.

Thus, Reason (R) is correct.

Relationship Between Assertion and Reason:

The Reason (R) correctly explains why the wavelength decreases in a denser medium, which leads to a reduction in fringe width and causes the fringes to come closer. Therefore, Reason (R) is the correct explanation for Assertion (A).