In an arrangement to view the interference pattern produced by a wedge of liquid between a microscope slide and a glass block thhe interference pattern obtained is made is equal spaced parallel fringes. The fringe separation (or fringe width) can not be decreased by which of the following actions.

Options

A. by increasing the angle of the liquid wedge
B. by unig a liquid of smaller refractive index.
C. by using a thicker glass block.
D. by unimg a longer liquid wedge of the same angle.

Explanation

To solve the problem of determining which action cannot decrease the fringe separation in an interference pattern produced by a wedge of liquid, we will analyze the relationship between fringe width and various factors involved in the setup.

### Step-by-Step Solution:

1. **Understanding Fringe Width**: The fringe width (or fringe separation) in an interference pattern is given by the formula:
\[ \text{Fringe Width} (W) = \frac{\lambda L}{d} \]
where:
- \( \lambda \) = wavelength of light used
- \( L \) = length of the wedge
- \( d \) = distance between the fringes

2. **Effect of Increasing the Angle of the Liquid Wedge**:
- Increasing the angle of the wedge will increase the distance \( d \) between the fringes.
- Since \( W \) is inversely proportional to \( d \), increasing \( d \) will decrease \( W \).
- **Conclusion**: This action can decrease the fringe width.

3. **Effect of Using a Liquid with a Smaller Refractive Index**:
- The fringe width is inversely related to the refractive index \( n \) of the liquid.
- If we decrease the refractive index, the fringe width \( W \) will increase.
- **Conclusion**: This action cannot decrease the fringe width.

4. **Effect of Using a Thicker Glass Block**:
- The fringe width is directly proportional to the thickness of the glass block.
- Increasing the thickness will increase the fringe width.
- **Conclusion**: This action cannot decrease the fringe width.

5. **Effect of Using a Longer Liquid Wedge**:
- The fringe width is directly proportional to the length of the wedge \( L \).
- Increasing \( L \) will increase the fringe width.
- **Conclusion**: This action cannot decrease the fringe width.

### Final Answer:
The actions that cannot decrease the fringe separation are:
- Using a liquid with a smaller refractive index.
- Using a thicker glass block.
- Using a longer liquid wedge.