Calculate the corrected staff reading at point A if the observed reading taken from an instrument set at 1.5 km from point A is 3.46 m.
Correct Answer: B. 3.3 m
📚 Detailed Explanation: Corrected Staff Reading at 1.5 km = 3.3 m
Why B (3.3 m) is correct: When the instrument is 1.5 km from the staff, the combined curvature and refraction effect makes the observed reading appear too large. Subtracting the combined correction from the observed reading gives the true (corrected) staff reading.
Formula: Corrected reading = Observed reading – Combined correction
Combined correction = 0.0673 × D² (D in km)
Combined correction = 0.0673 × D² (D in km)
D = 1.5 km
Combined correction = 0.0673 × (1.5)² = 0.0673 × 2.25 = 0.151425 ≈ 0.1514 m
Corrected reading = 3.46 – 0.1514 = 3.3086 ≈ 3.3 m
Effect of Curvature and Refraction on Staff Readings
| Effect | Direction | Impact on Reading |
|---|---|---|
| Earth curvature | Ground curves away below horizontal line of sight | Observed reading is LARGER than true value |
| Atmospheric refraction | Bends light ray downward; partially corrects curvature | Partially reduces the curvature error (1/7 of it) |
| Net combined effect | Reading still too large | Must subtract 0.0673 × D² from observed reading |
- Combined correction = 0.0673 × 1.5² = 0.1514 m (subtract from reading).
- Corrected reading = 3.46 − 0.1514 = 3.3 m.
- Without correction, the RL computed would be too low (the reading appeared too large).