Answer to Question #149383 in Physics for Francis

Question

A photographer takes a photograph of a Boeing 747 airliner Length 70.7 m) when it is flying directly overhead at an altitude of 9.50 km. The lens has a focal length of 5.00 m. How long is the image of the airliner on the film?

Answer 1

The linear magnification of an imaging system using a single lens is given by (for our purpose sign does not matter):

$$M = \left|\dfrac{f}{f-S_o}\right|$$

where $S_o = 9.5 km = 9500m$ is the distance from the lens to the object, and $f = 5m$ is the focal length of the lens. Thus, obtain:

$$M = \left|\dfrac{5m}{5m-9500m} \right|\approx 5.3\times 10^{-4}$$

This means that the object in the image is $M$ times smaller then it is in reality. Thus, if the actual lenght of the plane is $L = 70.7m$, then its length on the image is:

$$l = LM = 70.7m\cdot 5.3\cdot 10^{-4} \approx 0.037 m = 3.7cm$$

Answer. 3.7 cm.