A:When the apparatus of YDSE is brought in a liquid from air, the fringe width decreases.
R: The wavelength of light decreases in the liquid.

Options

A. IF both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark(2)
C. IF Assertion is true statement but Reason is false then mark(3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the given problem, we need to analyze the assertion (A) and the reason (R) provided in the question regarding Young's Double Slit Experiment (YDSE) when the apparatus is submerged in a liquid.

### Step-by-Step Solution:

1. **Understanding Fringe Width (β)**:
The fringe width (β) in YDSE is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) is the wavelength of light,
- \( D \) is the distance from the slits to the screen,
- \( d \) is the distance between the slits.

2. **Effect of Submerging in Liquid**:
When the YDSE apparatus is submerged in a liquid, the wavelength of light changes. The new wavelength (λ') in the liquid is given by:
\[ \lambda' = \frac{\lambda}{\mu} \]
where \( \mu \) is the refractive index of the liquid. Since \( \mu > 1 \) for any medium other than vacuum, the wavelength decreases when submerged in the liquid.

3. **Calculating New Fringe Width (β')**:
The new fringe width (β') when submerged in the liquid can be calculated using the modified wavelength:
\[ \beta' = \frac{\lambda' D}{d} = \frac{\left(\frac{\lambda}{\mu}\right) D}{d} = \frac{\lambda D}{\mu d} = \frac{\beta}{\mu} \]
Since \( \mu > 1 \), it follows that \( \beta' < \beta \). Therefore, the fringe width decreases when the apparatus is submerged in the liquid.

4. **Conclusion**:
- The assertion (A) that the fringe width decreases when the apparatus is brought in a liquid is correct.
- The reason (R) that the wavelength of light decreases in the liquid is also correct and explains the assertion.

### Final Answer:
Both the assertion (A) and the reason (R) are correct, and the reason correctly explains the assertion.