Answer to Question #239659 in Physics for Gbosky

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? Also how is the magnification affected?

Answer 1

Draw the figure:

We have two similar triangles here: one is large, created by the object and its rays, 1m-long and 50m-high, another is the triangle formed by the image and its ray diagram, h m high and 0.2 long. Write a proportion:

$$\frac{50}{1}=\frac{h}{0.2},\\\space\\ h=\frac{50·0. 2}{1}=10\text{ m}.$$

Magnification is the ratio of image height to object height:

$$M=\frac {h}{50}=0.2.$$

If the object distance is doubled, similarly, we have the following:

$$\frac{50}{2}=\frac{h}{0.2},\\\space\\ h=\frac{50·0. 2}{2}=5\text{ m}.\\\space\\ M=\frac5{50}=0.1.$$