# How a vernier caliper works?

Principle of the vernier scale is that a certain number of divisions(n) on the vernier scale is equal in length to a different number (usually one less, n-1) of main-scale divisions.          ie;     nV = (n − 1)S
n- number of divisions of vernier scale
V- one vernier scale division
S -one main scale division

least count = one main scale division/ number of vernier scale divisions

Figure shows a vernier caliper of 0.1 mm least count in which 0.0 to 1.0 on main scale shows 1 cm. The 10 marks on the vernier scale exactly coincide with 0.9 marks of main scale ie;  at 9 mm. So one division of vernier scale will be exactly .9 mm. If we measure a object of thickness 0.1 mm then the vernier scale will move 0.1 mm along the main scale. So first division of vernier scale at
0.9 mm+ 0.1 mm= 1mm on the main scale. That is exactly coincide with 1 mm of main scale.
measurement = main scale reading +(vernier scale reading × least count)
= 0 + ( 1 × .1) = 0.1 mm
Similarly when we measure 0.2 mm the vernier scale displaced by 0.2 mm and second division of vernier scale coincides with main scale (2 × 0.9 + 0.2 = 2 mm) at 2mm.

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