In levelling, what is the combined correction (curvature and refraction) at a distance of 1 km ?
- A6·7 × 10⁻⁶ m
- B0·067 mCorrect
- C167·5 m
- D670 m
Solution
Concept
Combined correction
Formula
C = 0.0673 d² (d in km, C in m)
Step-by-step solution
1. Curvature = 0.0785 d², refraction = 0.0112 d². 2. Combined = 0.0673 d² = 0.0673 × 1² = 0.0673 m ≈ 0.067 m.
Explanation
Curvature raises the apparent level and refraction lowers it partly, so the combined correction is subtractive with magnitude 0.0673 d².
Why the other options are wrong
The other values are 10⁴ or 10⁻⁵ times the right value.
Shortcut
0.0673 d² metres (d in km).
Common mistake
Entering the distance in metres.
Correct answer: B) 0·067 m