If the image of a triangulation station of R.L. 500 m is 4 cm from the principal point of a vertical photo taken from an altitude of 2000 m, above datum, the height displacement will be A. 2 mm B. 4 mm C. 6 mm D. 10 mm

2 mm
4 mm
6 mm
10 mm

The correct answer is $\boxed{\text{C}}$.

The height displacement is given by the following formula:

$$h = \frac{f}{z}d$$

where $h$ is the height displacement, $f$ is the focal length of the camera, $z$ is the flying height, and $d$ is the ground distance from the principal point to the object.

In this case, we have $f = 100 \text{ mm}$, $z = 2000 \text{ m}$, and $d = 4 \text{ cm} = 0.04 \text{ m}$. Substituting these values into the formula, we get:

$$h = \frac{100 \text{ mm}}{2000 \text{ m}} \times 0.04 \text{ m} = 0.02 \text{ m} = 2 \text{ mm}$$

Therefore, the height displacement is 2

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mm.

Option A is incorrect because it is half the correct answer. Option B is incorrect because it is the same as the correct answer. Option D is incorrect because it is twice the correct answer.