A microscope has its main scale with 20 divisions in 1 cm and vernier scale with 25 divisions, the length of which is equal to the length of 24 divisions of main scale. The least count of microscope is :

1. 0.002 cm
2. 0.001 cm
3. 0.02 cm
4. 0.01 cm

0.002 cm

Reason — The value of one main scale division x = $\dfrac{1}{20}$ cm

The number of divisions on vernier scale n = 25

Using the formula given below,

$\text{Least count (L.C.)} = \dfrac{\text{ Value of 1 main scale div (x)}}{\text {total no. of div on vernier(n)}}$

we get,

$\text {L.C.} = \dfrac{\text{x}}{\text{n}} \\[0.5em] \text{L.C.} = \dfrac{\dfrac{\text{1}}{\text{20}}}{25}\text{ cm} \\[0.5em] \text{L.C.} = \dfrac{\text{1}}{\text{500}}\text{ cm} \\[0.5em] \Rightarrow \text{L.C.} = 0.002\text{ cm} \\[0.5em]$

Hence, least count of microscope is 0.002 cm.