Vernier Scale

VERNIER SCALE

Vernier scale is also used to represent three consecutive units like diagonal scale. Vernier scale is the modified form of diagonal scale. It is used to measure very small units with greater accuracy. A vernier scale consists of : 

1. A primary long scale similar to a plain scale called “main scale”, which is fully divided into minor divisions.

2. A secondary short scale called "Vernier scale” used to read third unit which is a fraction of the second unit on the main scale.

The divisions on main scale and vernier scale are called as main scale division (msd) and vernier scale division (vsd) respectively. The difference between a main scale division and a vernier scale division gives the smallest length that can be measured using the vernier scale. This smallest length that can be measured is called the least count of vernier.

Vernier scale slides on the main scale. Both main scale and vernier scale combinedly used to measure three consecutive units. Vernier scales are mostly used in mechanical measuring instruments like vernier caliper, screw gauge etc. Two types of vernier scales are : 1. Backward vernier scale and 2. Forward vernier scale

Table : Comparison between Backward vernier scale and Forward vernier scale 

Example 8 :

Construct a vernier scale of R.F = 1/25 to show metre, decimetre and centimetre, to measure upto 4 metres. Mark a distance of 2.35 metres on the scale.

METHOD I: Backward Vernier Scale 

Data given : R. F = 1/25 ; Maximum length = 4m

Main unit, second unit and third unit (ie., vernier unit) are metre, decimetre and centimetre. 

1. Length of scale, Ls = RF × Maximum length

= 1 / 25 × 4m = 1/25 × (4 × 100) cm = 16 cm 

2. Draw a rectangle having length AB = 16 cm and width 2 cm (assumed) 

3. Divide the length of scale (ie., 16 cm) into 4 equal parts so that each part will represent 1 metre. 

4. Mark o at the end of first main division and the other divisions as 1, 2 and 3 towards right. 

5. Divide all the main divisions into 10 equal parts so that each subdivision will represent 1 decimetre. Mark the subdivisions as 1, 2, 3 etc., from O towards left. Now each division represent 1/10 metre i.e., 0.1 m. (ie., the second unit of decimetre) 

6. Construct a vernier scale CD above the first main division by taking 11 main divisions (ie., 1.1m) and dividing it into 10 equal parts. Each vernier division represent 1/10 × 1.1 = 0.11 metre. Name the divisions of vernier scale in opposite direction as that of main scale (ie., from C to D).

7. The divisions 1, 2, 3 etc., on vernier from C to D represents 0.11, 0.22, 0.33 m etc., To mark 2.35m on the scale constructed take 5 divisions from C (ie., 5 x 0.11 = 0.55m) and 1.80 metre on the main scale. ie., 1 main unit and eight subdivisions on second main division as shown in Fig. 

The length 2.35m is marked on the scale as shown in Fig. 5.8.

METHOD II : Forward Vernier Scale

The above problem can be solved by Forward Vernier scale method as explained below: 

Follow Step 1 to Step 5 as that of Backward vernier scale method.

6. Construct a vernier scale CD above the first main division by taking 9 main divisions (ie., 0.9 m) and dividing it into 10 equal parts. Each vernier division represent in 1/10 × 0.9 = 0.09 metre. Name the divisions of vernier scale in same direction as that of main scale (ie., from D to C).

7. The divisions 1, 2, 3 etc., on vernier from D to C represents 0.09, 0.18, 0.27m etc., To mark 2.35 m on the scale constructed take 5 divisions from C (i.e., 5 × 0.09 = 0.45m) and 1.9 metre on the main scale. ie., 1 main unit and 9 subdivisions on second main division as shown in Fig. 5.9.