In normal YDSE experiment, match the following two coloums.
`{:(,"Column I",,"Column II"),("A","In YDSE apparatus is immersed in a liquid",,"p. fringe width will increase"),("B","When wavelength of light used in increased",,"q. fringe width will decrease"),("C","When distance between slits and screen (D) is increased",,"r. fringe width will remain constant"),("D","When distance between two slits (d) is increased",,"s. fringe pattern will disappear"):}`

Explanation

To solve the problem of matching the two columns related to the Young's Double Slit Experiment (YDSE), we will analyze each option in Column I and determine the corresponding effect on fringe width (β) in Column II. The formula for fringe width is given by:

\[ \beta = \frac{\lambda D}{d} \]

where:
- \( \beta \) = fringe width
- \( \lambda \) = wavelength of light
- \( D \) = distance from the slits to the screen
- \( d \) = distance between the slits

### Step-by-Step Solution:

1. **Option A: In YDSE apparatus is immersed in a liquid**
- When the apparatus is immersed in a liquid, the wavelength of light changes to \( \frac{\lambda}{\mu} \) (where \( \mu \) is the refractive index of the liquid).
- Therefore, the new fringe width becomes:
\[ \beta' = \frac{\frac{\lambda}{\mu} D}{d} = \frac{\lambda D}{\mu d} \]
- Since \( \mu > 1 \), the fringe width \( \beta' \) will decrease.
- **Match:** A → q (fringe width will decrease)

2. **Option B: When wavelength of light used is increased**
- If the wavelength \( \lambda \) is increased, then from the formula:
\[ \beta = \frac{\lambda D}{d} \]
- An increase in \( \lambda \) leads to an increase in \( \beta \).
- **Match:** B → p (fringe width will increase)

3. **Option C: When distance between slits and screen (D) is increased**
- Increasing \( D \) while keeping \( \lambda \) and \( d \) constant results in:
\[ \beta = \frac{\lambda D}{d} \]
- An increase in \( D \) also leads to an increase in \( \beta \).
- **Match:** C → p (fringe width will increase)

4. **Option D: When distance between two slits (d) is increased**
- If \( d \) is increased, the formula becomes:
\[ \beta = \frac{\lambda D}{d} \]
- An increase in \( d \) will decrease \( \beta \) since \( d \) is in the denominator.
- **Match:** D → q (fringe width will decrease)

### Summary of Matches:
- A → q (fringe width will decrease)
- B → p (fringe width will increase)
- C → p (fringe width will increase)
- D → q (fringe width will decrease)

### Final Matching:
- A → q
- B → p
- C → p
- D → q