In YDSE, water is filled in the space between the slits and screen. Then

Options

A. Fringe pattern shifts upward but fringe width remains unchanged
B. fringe width decreases and fringe pattern shifts upward
C. fringe width remains unchanged and central fringe does not shift
D. fringe width decreases and fringe pattern does not shift

Explanation

To solve the problem regarding the Young's Double Slit Experiment (YDSE) with water filled between the slits and the screen, we will analyze the effects on fringe width and fringe pattern.

### Step-by-Step Solution:

1. **Understanding Fringe Width**:
The fringe width (β) in YDSE 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 Water on Wavelength**:
When water is introduced between the slits and the screen, the effective wavelength of light changes. The new wavelength (λ') in a medium is given by:
\[ \lambda' = \frac{\lambda}{n} \]
where \( n \) is the refractive index of water (approximately 1.33).

3. **Calculating New Fringe Width**:
Substituting the new wavelength into the fringe width formula, we get:
\[ \beta' = \frac{\lambda' D}{d} = \frac{\left(\frac{\lambda}{n}\right) D}{d} = \frac{\lambda D}{nd} \]
Since \( n > 1 \), it follows that:
\[ \beta' < \beta \]
This means that the fringe width decreases when water is introduced.

4. **Effect on Fringe Pattern**:
The introduction of water affects the speed of light in the medium, but it does not create a lateral shift in the fringe pattern. The path difference remains the same across the entire setup, and thus, the fringe pattern does not shift laterally.

5. **Conclusion**:
Therefore, with water filled in the space between the slits and the screen:
- The fringe width decreases.
- There is no lateral shift in the fringe pattern.

### Final Answer:
The fringe width decreases, and the fringe pattern does not shift.