Given information:
- R.L. (Reduced Level) of the triangulation station = 500 m
- Distance from the principal point to the image of the triangulation station = 4 cm
- Altitude of the photo above datum = 2000 m

Calculation:
Step 1: Find the ground distance:
- We know that the distance from the principal point to the image is equivalent to the focal length of the camera, which is denoted by 'f'.
- The ground distance 'G' can be calculated using the formula: G = (f * H) / h
- Where H is the altitude of the photo above datum and h is the distance from the principal point to the image.
- Substituting the given values, G = (f * 2000) / 4

Step 2: Calculate the height displacement:
- The height displacement can be calculated using the formula: Height displacement = G - R.L.
- Substituting the values, Height displacement = (f * 2000) / 4 - 500

Step 3: Convert the height displacement to millimeters:
- Since the given height displacement is in meters, it needs to be converted to millimeters.
- Multiply the height displacement by 1000 to convert it to millimeters.

Step 4: Calculate the answer:
- Substitute the given values into the formula from Step 2 and convert the result to millimeters using Step 3.

Result:
The height displacement is 10 mm.

Explanation:
- The given question is related to aerial photogrammetry, where we are given the altitude of the camera above datum and the distance from the principal point to the image of a triangulation station.
- Using the formula derived from the geometry of the camera, we can calculate the ground distance between the camera and the triangulation station.
- The height displacement is then calculated by subtracting the R.L. of the triangulation station from the ground distance.
- Finally, the height displacement is converted to millimeters as per the given units in the answer choices.

Note:
- The final answer is 10 mm, which may vary depending on the accuracy of measurements and calculation.