Answer to Question #239747 in Physics for Nneamaka

Question

An object 50m tall is placed 1m in front of a pinhole camera with length 20cm. What is the height of the image and the magnification produced? If the object distance is doubled, what is the size of the image produced? And how is the magnification affected?

Answer 1

We have similar triangles with a 50-m long base and height of 1 m, and the smaller one inside the camera 0.2 m high and h m tall:

$$\frac{50}{1}=\frac{h}{0.2},\\\space\\ h=\frac{0.2·50}{1}=10\text{ m}.$$

Magnification is the size of the image to the size of the object:

$$M=10/50=0.2.$$

If the object distance is doubled, the image height is 5 m (use the proportion written above) and the magnification is

$$M=5/50=0.1.$$