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 :

We need to evaluate the Assertion and Reason about Young's double slit experiment in a denser medium.

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.

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 to screen, and d is the slit separation.

In a denser medium, the wavelength decreases: $$\lambda_{medium} = \frac{\lambda_{air}}{n}$$, where n is the refractive index (n > 1).

Since $$\lambda$$ decreases, the fringe width $$\beta$$ decreases, meaning fringes come closer. So Assertion (A) is TRUE.

In a denser medium, the speed of light is $$v = c/n$$, which is less than c. The frequency remains unchanged ($$f = f_0$$). This is correct because the relationship $$v = f\lambda$$ means that when v decreases and f stays the same, $$\lambda$$ must decrease. So Reason (R) is TRUE.

The reason that fringes come closer is that $$\lambda$$ decreases in the denser medium. The wavelength decreases precisely because the speed decreases while frequency stays constant (as stated in R). Therefore, R correctly explains A.

The correct answer is Option 2: Both (A) and (R) are true and (R) is the correct explanation of (A).