If v, t and $$\frac{{\text{f}}}{{\text{H}}}$$ are the ground speed of the aircraft, the shutter speed of the camera and the scale of the photograph respectively, then the amount of image displacement A. $${\text{i}} = \frac{{{\text{v}} \times {\text{t}} \times {\text{H}}}}{{\text{f}}}$$ B. $${\text{i}} = \frac{{{\text{v}} \times {\text{f}}}}{{{\text{t}} \times {\text{H}}}}$$ C. $${\text{i}} = {\text{v}} \times {\text{t}} \times \frac{{\text{f}}}{{\text{H}}}$$ D. $${\text{i}} = \frac{{{\text{t}} \times {\text{H}}}}{{{\text{v}} \times {\text{f}}}}$$

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

The amount of image displacement is the distance that the aircraft travels during the time that the shutter is open. This distance is equal to the ground speed of the aircraft times the shutter speed. The scale of the photograph is the ratio of the distance on the photograph to the actual distance. Therefore, the amount of image displacement is equal to the ground speed of the aircraft times the shutter speed times the scale of the photograph.

Option A is incorrect because it does not include the scale of the photograph. Option B is incorrect because it divides the ground speed of the aircraft by the shutter speed, which would give the distance that the aircraft travels in one second. Option D is incorrect because it divides the shutter speed by the ground speed of the aircraft, which would give the time that the shutter is open for one unit of distance.