In YDSE, the sources is place symmetrical to the slits. If a transparent slab is placed in front of the upper slit, then

Options

A. intensity of central maxima may change
B. intensity of central maxima may not change
C. central maxima will be shifted up
D. intensity of dark fringe will be always zero

Explanation

To solve the problem regarding the Young's Double Slit Experiment (YDSE) with a transparent slab placed in front of the upper slit, we can break down the solution into the following steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- In the YDSE, we have two slits (let's call them S1 and S2) and a light source placed symmetrically to these slits. A transparent slab is placed in front of the upper slit (S1).

2. **Effect of the Transparent Slab**:
- The transparent slab can absorb some light, which may change the intensity of the light coming from the upper slit (S1). This absorption can affect the overall intensity of the interference pattern.

3. **Intensity of Light**:
- The intensity of the resultant light (IR) at any point on the screen is given by the formula:
\[ I_R = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos(\phi) \]
- Here, \(I_1\) is the intensity from the upper slit (S1), \(I_2\) is the intensity from the lower slit (S2), and \(\phi\) is the phase difference between the two waves.

4. **Change in Intensities**:
- If the slab absorbs some light, \(I_1\) will decrease, which will consequently affect the resultant intensity \(I_R\). Therefore, the intensity of the central maximum may change.

5. **Central Maximum Shift**:
- The introduction of a slab introduces an additional optical path difference. The path difference due to the slab is given by:
\[ \Delta x = (n - 1)T \]
- Here, \(n\) is the refractive index of the slab and \(T\) is the thickness of the slab. Since \(n > 1\), this path difference is positive, which means the central maximum will shift.

6. **Intensity of Dark Fringe**:
- The intensity of the dark fringe depends on the intensities \(I_1\) and \(I_2\). Since \(I_1\) may change due to the slab, the intensity of the dark fringe will not always be zero. It can vary based on the absorption characteristics of the slab.

### Conclusion:
From the analysis, we conclude:
- **Option A**: The intensity of the central maximum may change - **Correct**.
- **Option B**: The intensity of the central maximum may not change if the slab does not absorb light - **Correct**.
- **Option C**: The central maximum will be shifted up due to the introduction of the slab - **Correct**.
- **Option D**: The intensity of the dark fringe will not always be zero - **Incorrect**.

Thus, the correct options are A, B, and C.