Calculate the number of divisions of the main scale that is equal to the 8 divisions of the extended vernier.
📝 Detailed Explanation: The Extended Vernier
Vernier scales are ingenious devices for measuring more precisely than a standalone graduated scale. While direct and retrograde verniers are most common, the extended vernier is a special type designed for easy reading without being too long.
The defining characteristic of an extended vernier is its mathematical relationship between the vernier scale divisions and the main scale divisions.
⚙️ The Governing Formula
For an extended vernier, the relationship is defined as:
Formula
n divisions on Vernier Scale = (2n - 1) divisions on Main Scale
Where 'n' is the number of divisions on the vernier scale.
Applying the Formula to the Question:
We are given the number of divisions on the extended vernier and asked to find the corresponding number of divisions on the main scale.
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Identify the given value:
Number of vernier divisions, n = 8
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Apply the formula for main scale divisions:
Main Scale Divisions = 2n - 1
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Substitute and calculate:
Main Scale Divisions = (2 × 8) - 1
Main Scale Divisions = 16 - 1 = 15
Therefore, 8 divisions of this extended vernier are equal in length to 15 divisions of the main scale.
💡 Comparison with Other Vernier Types
- Direct Vernier: `n` vernier divisions = `(n-1)` main scale divisions. (e.g., 10 VSD = 9 MSD)
- Retrograde Vernier: `n` vernier divisions = `(n+1)` main scale divisions. (e.g., 10 VSD = 11 MSD)
- Extended Vernier: `n` vernier divisions = `(2n-1)` main scale divisions. (e.g., 8 VSD = 15 MSD)
The extended vernier is unique because the divisions on the vernier are much larger (almost double) than the divisions on the main scale, making it very clear to read.