The combined effect of Earth's curvature and the effect of refraction (in meters) for height observations is equal to which expression?

• A. 0.0675K2
• B. 0.0785K2
• C. 0.0110K2
• D. 0.0990K2

Answer: (A)

When you measure heights over a distance, two effects bend the line of sight: Earth’s curvature makes the line drop, and atmospheric refraction bends light downward, reducing that drop. The practical way to account for both is to use a quadratic correction in the distance: the farther you look, the larger the correction, proportional to the square of the distance.

For standard atmospheric conditions, curvature alone would give about 0.0785 meters per kilometer squared. Refraction lowers that total a bit, and the commonly used combined value is 0.0675 meters per kilometer squared. So the combined effect on a height observation is 0.0675 K^2 meters, where K is the distance in kilometers. For example, at 1 km, the correction is about 6.75 cm, a bit less than the curvature-only value, reflecting the refraction offset.