Understanding Combined Correction in Surveying

In surveying, when determining the level of a point, corrections are often needed due to the curvature of the Earth and the refraction of light rays in the atmosphere. These two corrections are often combined into a single value known as the combined correction for curvature and refraction.

Calculating the Combined Correction for 2 km Distance

The combined correction ($C$) for curvature and refraction can be calculated using an approximate formula when the distance ($D$) is given in kilometers and the result is desired in meters. The formula is:

$\qquad C = 0.0673 \times D^2$

Where:

• $C$ is the combined correction in meters.
• $D$ is the distance from the instrument to the point in kilometers.

In this specific question, the distance ($D$) given is 2 km.

Let's substitute the distance value into the formula:

$\qquad C = 0.0673 \times (2 \text{ km})^2$

First, calculate the square of the distance:

$\qquad (2 \text{ km})^2 = 4 \text{ km}^2$

Now, multiply this by the constant 0.0673:

$\qquad C = 0.0673 \times 4$

$\qquad C = 0.2692 \text{ m}$

So, the combined correction for curvature and refraction for a point located at a 2 km distance is 0.2692 meters.

Comparing with Options

Let's compare our calculated value with the given options:

Our calculated combined correction of 0.2692 m matches Option 1.

Conclusion

Using the standard formula for combined correction, $C = 0.0673 \times D^2$, with a distance $D = 2$ km, the resulting combined correction is 0.2692 m. This value represents the total adjustment needed due to the Earth's curvature and atmospheric refraction over that distance.