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Question
A microscope is provided with a main scale graduated with 20 divisions in 1 cm and a vernier scale with 50 division on it of length same as of 49 divisions of main scale. Find the least count of the microscope.
Solution
Given :
50 × vernier scale division (vsd) = 49 × main scale division (msd)
∴ 1 vsd = `49/50` msd = 0.98 msd
∴ least count = 1msd - 1 vsd
∴ least count = 1 msd - 0.98 msd = 0.02 msd....(1)
∴ 1 msd = `1/20` cm = 0.05 cm
⇒ least count = 0.02 × 0.05 cm = 0.001 cm
Thus, the least count of the microscope is 0.001 cm.
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