Ratios and Division

Students are often asked to compute many different ratios for no reason that is meaningful to them beyond general statements like "practice makes perfect." In the present setting, it is worthwhile to compute many different ratios. The basic idea is to fix a slide at a given distance from a light source and a wall or movie screen. The slide and the wall should be parallel. We are interested in how much different parts of an image on a slide are magnified by this projection. Choose several different pairs of points on the slide. Measure the distance between the two points in each pair on the slide. Then measure the distance between the two points in each pair on the wall. Find the ratio of these two distances. Compare this ratio with the ratio between the distance from the light source to the wall and the distance from the light source to the slide. These ratios should all be the same. Repeat the same experiment with the slide, light source, and wall in different positions. What happens if the slide and the wall are not parallel?