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 :

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

Both (A) and (R) are true but (R) is not the correct explanation of (A)

Wave Optics PYQ — JEE Main 2025 · 22 Jan · Shift 1 · Q68 with Solution

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Correct answer: C

Fringe width in Young’s double slit experiment

The fringe width is given by $\beta = \frac{\lambda D}{d}$ where:
- $\lambda$ = wavelength of light in the medium,
- $D$ = distance of screen from slits,
- $d$ = slit separation.
Effect of optically denser medium

In an optically denser medium of refractive index $\mu$ , $v = \frac{c}{\mu}$ Since frequency does not change on entering another medium, $\lambda' = \frac{v}{f} = \frac{c/\mu}{f} = \frac{\lambda}{\mu}$

So the wavelength decreases in the denser medium.
Effect on fringe width

Now, $\beta' = \frac{\lambda' D}{d} = \frac{\lambda D}{\mu d} = \frac{\beta}{\mu}$

Since $\mu > 1$ for an optically denser medium, $\beta' < \beta$

Therefore, the consecutive fringes come closer.

Hence, Assertion (A) is true.
Check the Reason (R)

The reason states that in an optically denser medium, speed of light reduces while frequency remains unchanged.

This is true.
Is (R) the correct explanation of (A)?

Yes. Because reduced speed with unchanged frequency implies reduced wavelength, and fringe width depends directly on wavelength: $\beta \propto \lambda$ Therefore fringes come closer.
Option analysis
- A: (A) false, (R) true $\rightarrow$ Incorrect
- B: Both true, but (R) not correct explanation $\rightarrow$ Incorrect
- C: Both true, and (R) is the correct explanation $\rightarrow$ Correct
- D: (A) true, (R) false $\rightarrow$ Incorrect

Final Answer: Option C.