Introduction:
The refractive index of a material is a measure of how much light slows down when it passes through that material. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material. To determine the refractive index of a glass slab using a travelling microscope, we need to perform a few measurements and calculations.

Procedure:
1. Place the glass slab on a flat surface.
2. Set up the travelling microscope in a way that the crosswire is visible through the glass slab.
3. Adjust the microscope to focus on the crosswire.
4. Measure the distance between the crosswire and the glass slab using the microscope's scale.

Explanation:
To determine the refractive index of the glass slab, we need to measure the thickness of the slab and the apparent shift in the position of the crosswire when viewed through the glass slab. The minimum number of readings required is three.

1. First Reading:
- Measure the distance between the crosswire and the glass slab when the microscope is not in contact with the slab.
- This reading gives us the initial position of the crosswire.

2. Second Reading:
- Lower the microscope until it is in contact with the upper surface of the glass slab.
- Measure the distance between the crosswire and the glass slab using the microscope's scale.
- This reading gives us the apparent position of the crosswire when viewed through the glass slab.

3. Third Reading:
- Raise the microscope until it is in contact with the lower surface of the glass slab.
- Measure the distance between the crosswire and the glass slab using the microscope's scale.
- This reading gives us the apparent position of the crosswire when viewed through the glass slab from the other side.

Calculation:
Using the three readings, we can calculate the refractive index of the glass slab using the formula:
Refractive Index = (Apparent Shift in Position)/(Thickness of the Glass Slab)

Conclusion:
Therefore, the minimum number of readings required to determine the refractive index of a glass slab using a travelling microscope is three. These readings are necessary to calculate the apparent shift in position and the thickness of the glass slab.