In levelling, when correcting for errors due to both the curvature of the Earth and atmospheric refraction, which of the following statements is/are correct? i. The curvature correction accounts for the line of sight deviating from a horizontal plane due to the Earth’s curvature, while the refraction correction accounts for the bending of light rays in the atmosphere, with refraction usually reducing the overall error caused by the curvature. ii. The curvature correction is generally larger than the refraction correction, and refraction correction is always subtracted from the curvature correction. iii. Both curvature and refraction errors are directly proportional to the distance, but refraction error is typically greater than the curvature error over long distances.
- AOnly (i)
- BOnly (i) and (ii)Correct
- COnly (ii) and (iii)
- D(i), (ii) and (iii)
Solution
Concept
Curvature and refraction corrections in levelling
Formula
NONE
Step-by-step solution
1. Curvature correction accounts for line of sight deviation due to Earth curvature, whereas atmospheric refraction bends light rays downward, partially counteracting curvature error. 2. Refraction correction reduces the curvature error effect by approximately one-seventh over standard distances. 3. Therefore, statement i correctly describes the working principles of both corrections. Answer: B
Explanation
Atmospheric refraction causes light rays to bend downward toward the Earth's surface, which partially offsets the upward error caused by Earth's curvature. Curvature correction is significantly larger than refraction correction, meaning refraction correction is subtracted from curvature correction to obtain the combined correction, and both errors vary with the square of distance rather than linearly. Thus, statements i and ii are true while statement iii is false, making option B the correct answer.
Why the other options are wrong
C) Statement (iii) is false because refraction error is typically smaller than curvature error. D) Statements (ii) and (iii) are false.
Shortcut
Curvature error (D²/2R) is larger than refraction error (1/7 of curvature) and subtracted from readings.
Common mistake
Selecting option D instead of B by incorrectly believing atmospheric refraction error is greater than curvature error over long distances.
Correct answer: B) Only (i) and (ii)