Question

The veriner scale of a travelling microscope has 50 division which coincide with 49 main scale divisions. If each main scale division is 0.5 mm, calculate the minimum inaccurancy in the measurement of distance.

Answer 1

the least count = 1/50.

so precision in measurements  =  1/50 * 0.5 mm = 0.01 mm
49 main scale divisions = 49 * 0.5 mm = 24.5 mm.
50 Vernier scale divisions = 24.5 mm => each vernier scale division = 24.5/50 = 0.49 mm
the difference between the lengths of one main scale division and one vernier scale division = 0.50 - 0.49 mm = 0.01 mm.
This is the least count of the Vernier scale. When you measure the length of an object, the length is measurable up to an accuracy of 0.01 mm. 
Suppose we have an object of length 2.11 mm. We put that in the Vernier calipers. Then we read the vernier scale. That will match with the main scale at the 11th division... On the main scale it will read 15 divisions. It means 7.50 mm.. On the vernier scale 11 divisions means 11 * 0.49mm = 5.39 mm... Subtracting 5.39 mm from 7.50 mm , we get the length of the object as 2.11 mm. 
the formula is : precision or least count = 1 main scale division / number of divisions on the Vernier scale. 
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