Question

3. A microsocpe is provided with a main scale
graduated with 20 divisions in 1 cm and a vernier
scale with 50 divisions on it of length same as of
49 divisions of main scale. Find the least count of
the microscope
​

Answer 1

50 × vernier scale division (vsd) = 49 × main scale division (msd)

∴ 1 vsd = $\sf \dfrac{49}{50} msd$ = 0.98 msd

∴ least count = 1msd - 1 vsd

∴ least count = 1 msd - 0.98 msd = 0.02 msd ....(1)

∴ 1 msd = $\sf \dfrac{1}{20}cm$ = 0.05cm

⇒ least count = 0.02 × 0.05 cm = 0.001cm

Thus, the least count of the microscope is 0.001cm.