Which of the followig inctruemnts has minium least count?

Explanation

To determine which instrument has the minimum least count, we will calculate the least count for each of the three options provided.

### Step-by-Step Solution:

1. **Understanding Least Count**: The least count of an instrument is defined as the smallest value that can be measured accurately with that instrument. It is calculated using the formula:
\[ \text{Least Count} = \frac{\text{Pitch}}{\text{Number of Divisions}} \]

2. **Calculate Least Count for the Screw Gauge**:
- Given: Pitch = 1 mm and Number of Divisions = 100
- Convert pitch to centimeters: \(1 \text{ mm} = 0.1 \text{ cm}\)
- Now, apply the formula:
\[ \text{Least Count}_{\text{screw gauge}} = \frac{0.1 \text{ cm}}{100} = 0.001 \text{ cm} \]

3. **Calculate Least Count for the Spherometer**:
- Given: Pitch = 0.1 mm and Number of Divisions = 100
- Convert pitch to centimeters: \(0.1 \text{ mm} = 0.01 \text{ cm}\)
- Now, apply the formula:
\[ \text{Least Count}_{\text{spherometer}} = \frac{0.01 \text{ cm}}{100} = 0.0001 \text{ cm} \]

4. **Calculate Least Count for the Optical Instrument**:
- The least count is determined by the wavelength of light, which is approximately \(10^{-5} \text{ cm}\) or \(0.00001 \text{ cm}\).
- Therefore, the least count for the optical instrument is:
\[ \text{Least Count}_{\text{optical}} = 0.00001 \text{ cm} \]

5. **Comparison of Least Counts**:
- Least Count of Screw Gauge: \(0.001 \text{ cm}\)
- Least Count of Spherometer: \(0.0001 \text{ cm}\)
- Least Count of Optical Instrument: \(0.00001 \text{ cm}\)

6. **Conclusion**:
- The optical instrument has the minimum least count of \(0.00001 \text{ cm}\). Therefore, the correct answer is that the optical instrument has the minimum least count.

### Final Answer:
The optical instrument has the minimum least count.