Correct : a
In reciprocal levelling across a wide valley, both observations are affected by the combined error due to earth''s curvature and atmospheric refraction. Let h be the true difference in level (Q − P) and e be the combined error. Since refraction is the same for both observations and the distance PQ is the same, e is identical for both.
When the instrument is stationed near P, the error e makes Q appear higher than its true level:
Observed (Q − P) = h + e = 3.0 m ... (i)
When the instrument is stationed near Q, the same error e makes P appear higher, so Q appears lower:
Observed (Q − P) = h − e = −1.0 m ... (ii)
Adding both equations:
2h = 3.0 + (−1.0) = 2.0
h = 1.0 m (Q is 1.0 m above P)
This is the standard reciprocal levelling formula: true difference = average of the two observed differences = (3.0 + (−1.0))/2 = 1.0 m ✓
Correct answer: A — 1.0 m ✓
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