Assertion: if a glass slab is placed in front of one of the slits, then fringe with will decreases.
Reason: Glass slab with produce an additional path difference.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that if a glass slab is placed in front of one of the slits, then the fringe width decreases.

**Hint:** Consider what happens to the interference pattern when a medium with a different refractive index is introduced.

### Step 2: Analyze the Effect of the Glass Slab
When a glass slab is placed in front of one of the slits, it introduces a change in the optical path length due to its refractive index. The additional path difference created by the glass slab can be calculated using the formula:
\[ \text{Path Difference} = (n - 1) \times t \]
where \( n \) is the refractive index of the glass and \( t \) is the thickness of the glass slab.

**Hint:** Think about how this additional path difference affects the interference pattern.

### Step 3: Understand Fringe Width
Fringe width (\( \beta \)) in a double-slit experiment is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where \( \lambda \) is the wavelength of light used, \( D \) is the distance from the slits to the screen, and \( d \) is the distance between the slits.

**Hint:** Identify which parameters in the fringe width formula are affected by the introduction of the glass slab.

### Step 4: Determine the Impact on Fringe Width
The introduction of the glass slab does not change the wavelength of the light (\( \lambda \)), the distance to the screen (\( D \)), or the distance between the slits (\( d \)). Therefore, the fringe width remains unchanged despite the introduction of the glass slab.

**Hint:** Reflect on how the path difference affects the position of the fringes but not their width.

### Step 5: Conclusion
Since the assertion claims that the fringe width decreases, and our analysis shows that the fringe width remains unchanged, the assertion is false. The reason states that the glass slab produces an additional path difference, which is true.

**Final Answer:** The assertion is false, and the reason is true. Therefore, the correct answer is D (Assertion is false, Reason is true).