The correct answer is $\boxed{\text{A. }1 : 10,000}$.
The scale of a photograph is the ratio of the distance between two objects on the photograph to the actual distance between those objects. In this case, the two objects are the camera and the ground. The distance between the camera and the ground is 300 m. The focal length of the camera is 15 cm. The focal length of a camera is the distance between the lens and the sensor when the camera is focused at infinity. The focal length determines the angle of view of the camera. A wider angle of view means that more of the scene will be captured in the photograph. A narrower angle of view means that less of the scene will be captured in the photograph.
To calculate the scale of the photograph, we need to know the focal length of the camera and the distance between the camera and the ground. We can use the following formula to calculate the scale:
$$\text{Scale} = \frac{f}{d}$$
where $f$ is the focal length of the camera in meters and $d$ is the distance between the camera and the ground in meters.
In this case, the focal length of the camera is 15 cm and the distance between the camera and the ground is 300 m. Substituting these values into the formula, we get:
$$\text{Scale} = \frac{0.15}{300} = 0.0005 = 1 : 10,000$$
Therefore, the scale of the photograph is 1 : 10,000. This means that every 1 cm on the photograph corresponds to an actual distance of 10,000 cm, or 100 m.