Vernier Scale

 

• Similar to Diagonal scale, Vernier scale is used for measuring up to second decimal.
• A Vernier scale consists of (i) a main scale  and (ii) a vernier.
• The main scale is a plain scale fully divided in to minor divisions. A subdivision on the mail scale is called the  main scale division (MSD) .
• The graduations on the vernier are derived from those on the primary scale. A subdivision on the verscale is called the vernier scale division (VSD).

Least Count  (LC)  is the minimum length that can be measured precisely by a given vernier scale. This can be determined by the following expression:
LC = MSD – VSD     ( if MSD > VSD)
LC = VSD  – MSD     ( if VSD > MSD)
The LC is mentioned as a fraction of the MSD.
If the MSD of a scale represents 1 mm and LC  is 0.1 mm,

LC = 0.1 mm  = (1/10) MSD

1. Assume MSD > VSD  
   LC = MSD –VSD
   1/10 MSD  = MSD –VSD
   i.e.,  VSD  = MSD – 1/10 MSD
   10 VSD  = 9 MSD
   i.e., Length of VSD  = 9 MSD.
   

This length must be divided in to 10 equal parts so that LC = 0.1 mm

2. Assume VSD > MSD
   LC = VSD – MSD
   1/10 MSD = VSD – MSD
   i.e.,  VSD = 1/10 MSD + MSD
   10 VSD = 11 MSD
   This length is to be divided in to 20 equal parts so that LC = 0.1 mm