In a Young's double-silt experiment the source slit S and the two slits A and B are horizontal with slit A above slit B. The fringe are observed on a vertical screen. The optical path length from S to B is increased slightly by introducing a tranparent slab. As a result the fringe pattern on the screen moves

Options

A. vertically downwards
B. vertically upwards
C. horizontally to the left
D. horizontally to the right

Answer

To solve the problem regarding the movement of the fringe pattern in a Young's double-slit experiment when a transparent slab is introduced in the path to slit B, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- In a Young's double-slit experiment, we have a light source (S) and two slits (A and B). The slits are horizontal, with slit A above slit B, and the interference pattern is observed on a vertical screen.

2. **Introducing the Transparent Slab**:
- A transparent slab is introduced in the path from the source (S) to slit B. This slab increases the optical path length for the light traveling through slit B.

3. **Effect on Optical Path Length**:
- The introduction of the slab means that light traveling to slit B will take longer to reach the screen compared to light traveling to slit A. The additional distance traveled by the light through the slab can be represented as an increase in the optical path length.

4. **Phase Difference**:
- The increase in optical path length results in a phase difference between the light waves coming from slits A and B. The phase difference (Δφ) can be calculated using the formula:
\[ \Delta \phi = \frac{2\pi}{\lambda} \Delta L \]
where ΔL is the additional path length introduced by the slab and λ is the wavelength of the light.

5. **Resulting Fringe Shift**:
- As a result of the increased phase difference, the interference pattern will shift. Since the light from slit B is delayed, the intensity of the light reaching the screen from slit A will dominate, causing the fringes to shift downward.

6. **Conclusion**:
- The fringe pattern on the screen will move vertically downwards due to the introduction of the transparent slab in the path to slit B.

### Final Answer:
The fringe pattern on the screen moves vertically downwards.