A microscope 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.

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Solution

Given:
1 main scale division = 1/20 cm
50 divisions of vernier scale = 49 divisions of main scale
1 division of vernier scale = 49 $\div$ 50 main scale divisions
= 0.98 main scale division
Vernier calipers:
L.C. = I main scale division - I vernier scale division
= I main scale division - 0.98 main scale division
= 0.02 main scale division
Microscope:
1 main scale division = 1/20 cm
L.C = 0.02 $\times$ 1/20 = 0.001 cm
$∴$ Least count of the microscope is $0.001 c m$

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