The effect of refraction (in meters) for height observations is equal to which expression, where K is the horizontal distance in kilometers?

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

Answer: (C)

The main idea here is that atmospheric refraction introduces a vertical error in height observations that grows with distance, and a simple practical model uses a quadratic dependence on the horizontal distance. In this model, the refraction effect in meters is given by a constant times the square of the distance in kilometers. The commonly used coefficient for standard conditions is 0.0110, so the correction is delta height = 0.0110 × K^2 meters, where K is the horizontal distance in kilometers. This means the error increases with distance, and doubling the distance makes the correction rise by a factor of four. For example, at 1 km the correction is about 0.011 m (roughly 1.1 cm), at 2 km about 0.044 m, and so on. The 0.0110 value aligns with average atmospheric refraction behavior used in height observations, making it the appropriate expression.