An aerial survey aircraft is equipped with a camera having a focal length of 20 cm . The camera uses a square image sensor of area 16 cm ^2 . If the camera needs to capture a square ground area of 64 km ^2 in a single frame, the required flight altitude of the aircraft is :

Step-by-step solution

Let the side length of the square image sensor be y and the side length of the ground area be x . Area of the image sensor, A_i = 16 cm ^2 y = 16 cm = 4 cm = 4 10⁻² m Area of the ground captured, A_o = 64 km ^2 x = 64 km = 8 km = 8 10^3 m The linear magnification m is given by the ratio of the image size to the object size: m = y x = 4 10⁻² 8 10^3 = 1 2 10^5 For a distant object, the image is formed at the focal plane, so the image distance v f . The magnification is also given by m = v u f H , where H is the fligh