Question

The combined effect of curvature and refraction is that the objects appear
1. higher than they really are
2. lower than they really are
3. Both (A) and (B) 
4. None of the above

Answer 1

Correct Answer - Option 2 : lower than they really are

Concept:

The RL of various points are generally taken by assuming level line is flat horizontal line, but actually it is a curve line. This difference between level line and horizontal line should be deducted from staff reading  This is called correction due to curvature of earth and it is given as:

C_c = 0.0785 × d² , Where d is the horizontal distance in km

Curvature Correction increases the staff reading i.e. it is negative for staff reading.

Due earth refraction, line of sight bends towards the earth, therefore we noted less value of staff of reading i.e. Decrease in staff reading. It is positive for staff reading. It is generally taken as one seventh of the correction due to curvature.

For staff reading:

Total correction = Curvature correction (C_c) + Correction due to refraction (C_r)

C_total = - C_c + C_c/7  

C_total = -(6/7)C_c

⇒ Curvature makes the staff point to appear low and thus a larger reading is obtained than the actual value and thus the correction is negative.