In Young's double-slit experiment, the slit are illuminated by monochromatic light. The entire set-up is immersed in pur water. Which of the following act cannot restore the oringinal fringe width?

Options

A. Bringing the slit close together.
B. Moving the screen away from the slit plane.
C. Replacing the incident light by that of longer wavelength.
D. Introducing a thin transparent slab in front of one of the slits.

Explanation

To solve the question regarding Young's double-slit experiment and the effect of immersing the setup in pure water, we need to analyze how different actions affect the fringe width (β). The formula for fringe width is given by:

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

where:
- \( \lambda \) = wavelength of light
- \( D \) = distance between the slits and the screen
- \( d \) = distance between the slits

When the entire setup is immersed in water, the wavelength of light changes due to the refractive index (μ) of water. The new wavelength in water is given by:

\[ \lambda' = \frac{\lambda}{\mu} \]

Thus, the formula for fringe width in water becomes:

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

Now, let's analyze each option provided in the question:

**Option A: Bringing the slits close together.**
- If the distance between the slits (d) decreases, then according to the formula, the fringe width (β) will increase because β is inversely proportional to d. Therefore, this action changes the original fringe width.

**Option B: Moving the screen away from the slit plane.**
- If the distance between the slits and the screen (D) increases, then the fringe width (β) will also increase since β is directly proportional to D. Thus, this action also changes the original fringe width.

**Option C: Replacing the incident light by a longer wavelength.**
- If the wavelength (λ) is increased, then the fringe width (β) will increase because β is directly proportional to λ. Therefore, this action changes the original fringe width as well.

**Option D: Introducing a thin transparent slab in front of one of the slits.**
- Introducing a thin slab will change the path length of light from that slit, but it does not affect the overall fringe width formula since the fringe width depends on the distance between the slits and the screen, the distance between the slits, and the wavelength in the medium. The introduction of a slab does not change these parameters. Therefore, this action does not change the original fringe width.

### Conclusion:
The actions that cannot restore the original fringe width are **Option D**. The options that do change the fringe width are **Option A, Option B, and Option C**.