Mirrors
Many children enjoy experimenting with mirrors in the nursery, and these children were experimenting with two mirrors placed at 90 degrees from each other. In the images below, you can see some of the children’s explorations.
In one of the images above, the children realised that they could see three images of a circle they placed before the mirror; this looked like there were four circles in total. They were able to see exactly three copies of the circle as the mirrors were placed at 90 degrees from each other. This meant that the children could see one whole reflection in each mirror and another reflection which happens as a result of the mirrors reflecting each other’s contents. At 90 degrees, these reflections of reflections align so that we get three images in total.
Children might find it interesting to change the angles between the two mirrors to see if they can increase the number of reflected images they can see. When the mirrors are at 90 degrees, the children can see 3 images of the object. If they were to decrease the angle between the mirrors to 60 degrees, they should be able to see 5 images of the object, as shown on the right-hand side of the image below.
There is a relationship between the number of images that can be seen and the angle between the two mirrors. If the children were to experiment with changing the angle between the mirrors, they would find the following results.
| Angle Between the Mirrors | Number of Images Seen |
|---|---|
| 180 | 1 |
| 120 | 2 |
| 90 | 3 |
| 72 | 4 |
| 60 | 5 |
| 51 | 6 |
| 45 | 7 |
The angle we need to find exactly a given number of whole images of an object is given by \(\text{angle } = \frac{360}{\text{number of images } + 1}\). Here, it is also important to mention that to achieve this effect, the object needs to be the same distance away from each mirror.
Infinite Images
Above, we thought about reducing the angle between two mirrors. Children might be interested in thinking about what happens when two mirrors are parallel. Here, an object will be reflected infinitely, meaning that the number of copies seems to go on forever. You might have seen this effect in a bathroom before when there are mirrors on opposite walls. There is a diagram of this happening below, when the object is closer to one mirror than the other, which leads to clustering behaviour.
Kalidoscopes
Angled mirrors are used in kaleidoscopes to reflect some movable objects. A common arrangement of mirrors inside a kaleidoscope is an equilateral triangular prism, as shown in the image below. This means that the mirrors will produce multiple reflections of the object and create the beautiful, symmetric patterns that kaleidoscopes are known for.
