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 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.