Question

Photographs of the ground are taken from an aircraft flying at an altitude of 2000 m by a camera with a lens of focal length 50 cm. The size of the film in the camera is $18cm\times 18cm.$ The area of the ground that can be photographed by the camera is:

• A. $720m\times 720m$
• B. $720cm\times 720cm$
• C. $360cm\times 360cm$
• D. None of these

Answer 1

The correct option is A $720m\times 720m$

$\frac{\text{Area of the image}}{\text{Area of the object}}=$ Aerial magnification $=m^2$
Where m is the linear magnification
$\therefore m=\frac{f}{f+u}=\frac{0.5}{0.5-2000}\approx -\frac{1}{4000}$
Now, area of the image is equal to size of the camera film, therefore
Area of object$=\frac{\text{Area of the image}}{m^2}$
$=18\times 18\times 4000\times 4000$
$=72000cm\times 72000cm$
Note that m has no unit, so area of object is in same units as area of image.