A : If the whole apparatus of Young.s experiment is immersed in liquid, the fringe width will decrease.
R : The wavelength of light in water is more than that in air.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of A
C. A is true and R is false
D. Both A and R are false

Answer

To solve the question regarding Young's experiment and the effects of immersing the apparatus in a liquid, we need to analyze both statements A and R.

### Step-by-Step Solution:

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

2. **Effect of Immersing in Liquid**:
When the entire apparatus is immersed in a liquid, the wavelength of light changes. The wavelength in a medium is given by:
\[ \lambda' = \frac{\lambda}{n} \]
where \( n \) is the refractive index of the liquid. For water, \( n \) is greater than 1, meaning the wavelength in water (\( \lambda' \)) is less than the wavelength in air (\( \lambda \)).

3. **Analyzing Statement A**:
Statement A claims that if the apparatus is immersed in liquid, the fringe width will decrease. Since the wavelength decreases when immersed in a liquid, and fringe width is directly proportional to the wavelength, it follows that:
\[ \text{If } \lambda \text{ decreases, then } \beta \text{ also decreases.} \]
Therefore, Statement A is **True**.

4. **Analyzing Statement R**:
Statement R claims that the wavelength of light in water is more than that in air. However, as we established, the wavelength of light in water is actually less than that in air due to the refractive index being greater than 1. Thus, Statement R is **False**.

5. **Conclusion**:
Since Statement A is true and Statement R is false, the correct answer is that A is true and R is false.

### Final Answer:
- A is true, R is false. Therefore, the correct option is C.