Reciprocal levelling eliminates which of the following errors?
Correct Answer: B. Collimation, curvature and refraction error
📚 Detailed Explanation: Reciprocal Levelling Eliminates Collimation, Curvature, and Refraction Errors
Why B (Collimation, curvature and refraction error) is correct: Reciprocal levelling takes readings from both sides of an obstacle. When the two apparent height differences are averaged, all systematic errors that affect both observations equally — including collimation, curvature, and refraction — cancel out completely.
Errors Cancelled by Reciprocal Levelling
| Error Type | How It Affects Single Reading | Cancelled by Reciprocal? |
|---|---|---|
| Collimation error | Line of sight not horizontal; larger error on the far staff (longer sight) | ✓ YES — the long sight alternates between A and B in the two setups; errors cancel in average |
| Earth curvature | Ground curves away; far staff reading is too large | ✓ YES — affects the far staff equally from both setups; cancels in average |
| Atmospheric refraction | Light bends downward; partially corrects curvature but introduces its own error on long sights | ✓ YES — same magnitude from both sides; cancels in average |
| Instrumental errors (non-systematic) | Random reading errors | ✗ NOT fully — only systematic errors cancel; random errors are averaged |
True height difference h:
h = [(Staff at B from A setup) – (Staff at A from B setup)] / 2
OR equivalently:
h = [(Apparent diff from A setup) + (Apparent diff from B setup)] / 2
h = [(Staff at B from A setup) – (Staff at A from B setup)] / 2
OR equivalently:
h = [(Apparent diff from A setup) + (Apparent diff from B setup)] / 2
Both collimation error, curvature, and refraction affect each “apparent diff” by the same amount
but in opposite effective directions when swapped — they cancel in the average.
- Reciprocal levelling cancels: collimation error + earth curvature + atmospheric refraction.
- Method: average of two apparent height differences (one from each side).
- Only systematic errors cancel; random reading errors are reduced but not eliminated.