Question

A photograph of a landscape is captured by a drone camera at a height of 18 km. The size of the camera film is 2 cm \( \times \) 2 cm and the area of the landscape photographed is 400 km\(^2\). The focal length of the lens in the drone camera is:

• A. \( 0.9 \, \text{cm} \)
• B. \( 2.8 \, \text{cm} \)
• C. \( 2.5 \, \text{cm} \)
• D. \( 1.8 \, \text{cm} \)

Hint:

To solve problems involving photographs and cameras, use the relationship between the image size, the actual size of the object, and the distance (height) from the object. This is a direct application of similar triangles.

Answer 1

The Correct Option is A

We use the formula for a camera to relate the size of the image, the size of the landscape, the height of the camera, and the focal length: \[ \frac{\text{Size of image}}{\text{Size of landscape}} = \frac{\text{Focal length}}{\text{Height of camera}}. \] Here, the size of the image is \( 2 \times 2 \) cm (so the area is 4 cm\(^2\)), the size of the landscape is 400 km\(^2\), and the height of the camera is 18 km. Substituting these values into the equation and solving for the focal length, we find that the focal length is \( 0.9 \, \text{cm} \). 
Final Answer: \( 0.9 \, \text{cm} \).