The vernier scale is a precise measuring tool used on instruments like vernier calipers, micrometres, and height gauges. Named after Pierre Vernier, who introduced it in the 17th century, the vernier scale allows users to measure with greater accuracy than a standard scale alone. By adding a secondary scale with finer divisions, the vernier scale helps increase measurement precision, reduce human estimation errors, and make readings more exact.
Key Components:
- Main Scale: Functions like a typical ruler, providing primary measurement divisions.
- Vernier Scale: A smaller, movable scale with increments that are a fraction of the main scale’s increments. When the vernier scale’s marks align with the main scale, it indicates a precise fractional measurement.
The difference between each division on the vernier scale and the main scale is called the least count or vernier constant—this represents the smallest measurement that can be precisely read with the instrument.
Working Principle
The vernier scale works on the principle of alignment:
- Alignment for Precision: As the vernier scale slides along the main scale, users look for the point where one line on the vernier scale exactly aligns with a line on the main scale.
- Reading Calculation: By identifying the aligned marks, the user can add this fractional measurement (shown by the vernier scale) to the main scale reading for a precise result.
For example, if the main scale reads 12mm, and the 3rd division on the vernier scale aligns with a main scale line, the measurement would be:
- Main Scale Reading: 12mm
- Vernier Scale Reading: 3 x 0.02mm = 0.06mm
- Total Measurement: 12mm + 0.06mm = 12.06mm
The length of ‘n’ divisions on the vernier scale is equal to n-1 divisions on the Main Scale.
10 divisions of MS = 10 mm
1 division of MS = 1mm
The vernier scale is one division less than the main scale (1 mm less)
Therefore:
10 divisions of VS = 9 mm
1 division of VS = 9/10 mm= 0.9 mm
Vernier Constant (Least Count)
The difference between one division on the main scale and one division on the vernier scale represents the least count (or vernier constant) of the instrument. This is the smallest measurement that can be accurately read with the vernier caliper.
Least Count = 1 division on MS – 1 division on VS
Least Count = 1 mm − 0.9 mm = 0.1 mm
The Least Count (LC) of a vernier caliper can also be expressed using the formula:
$$LC = \frac{1}{N} \times P$$
where:
- N is the total number of divisions on the vernier scale,
- P is the Pitch which represents the value of one division on the main scale.
This formula calculates the smallest measurable value or the “Least Count” by dividing the main scale’s division value by the number of divisions on the vernier scale. This gives the smallest difference that can be read between the main and vernier scales.
