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

The relationship between image size, landscape size, camera height, and focal length is expressed by the camera formula: \[ \frac{\text{Size of image}}{\text{Size of landscape}} = \frac{\text{Focal length}}{\text{Height of camera}}. \] Given an image size of \( 2 \times 2 \) cm (area 4 cm\(^2\)), a landscape size of 400 km\(^2\), and a camera height of 18 km, we can solve for the focal length. Substituting these values into the equation yields a focal length of \( 0.9 \, \text{cm} \).
Final Answer: \( 0.9 \, \text{cm} \).