To find the least count of the screw gauge, we first need to calculate its pitch. Pitch is the distance moved by the spindle per revolution. $\text{Pitch} = \frac{\text{Distance covered on the pitch scale}}{\text{Number of rotations}}$ $\text{Pitch} = \frac{1 \text{ mm}}{2} = 0.5 \text{ mm}$

The least count (LC) is given by the ratio of the pitch to the total number of divisions on the circular scale: $\text{Least Count} = \frac{\text{Pitch}}{\text{Total number of circular scale divisions}}$ $\text{LC} = \frac{0.5 \text{ mm}}{50} = 0.01 \text{ mm}$

Now, convert the least count into metres: $\text{LC} = 0.01 \times 10^{-3} \text{ m} = 10^{-5} \text{ m}$