What it shows
A single mirror stood on a shape shows its line of symmetry: half a butterfly becomes a whole one. Two mirrors hinged together show more and more copies as the angle closes: at 90 degrees you see 4 copies in all, at 60 degrees 6 copies and at 45 degrees 8 copies, always 360 divided by the angle.
The science
A mirror image is the same distance behind the mirror as the object is in front, so a shape placed against a mirror along its line of symmetry looks complete. With two mirrors, each image is reflected again in the other mirror, and the images sit round a circle at equal angles. The circle of 360 degrees is split into sectors the size of the mirror angle, so the number of copies, counting the object itself, is 360 divided by the angle.
Materials
Cost: under Rs 200. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- Two small plastic mirrors or mirror tiles about 10 cm square
- Cloth tape for the hinge
- A protractor drawn on a card base
- Paper shapes: half a butterfly, letters, a coin
- Coloured beads or bindis
Safety
For this project: Use plastic mirrors, or tape the edges of glass mirrors, and an adult must handle any glass.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Tape the two mirrors together along one edge so they open and close like a book, with the shiny sides facing in.
Draw a protractor on the card base with the hinge at the centre, so the mirror angle can be read.
Stand one mirror upright across the middle of a drawing of half a butterfly and watch it become whole. Try the letters A, B, H and S to find which have a line of symmetry.
Open the mirrors to 90 degrees, put a bead between them and count the beads you see, including the real one: 4.
Close to 60 degrees and count again: 6 copies. Close to 45 degrees: 8 copies. Record the angle and the count.
Work out 360 divided by each angle and compare with your count.
Put a few coloured bindis between the mirrors at 60 degrees to make a kaleidoscope pattern and photograph or draw it.
What you should see
The model shows which letters have a line of symmetry and gives 4, 6 and 8 copies at 90, 60 and 45 degrees, matching 360 divided by the angle.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1How many copies will you see at 30 degrees?
12, because 360 divided by 30 is 12.
2Which capital letters have a vertical line of symmetry?
Letters such as A, H, M, T, U, V, W, X and Y.
3Does the letter S have a line of symmetry?
No, but it has rotational symmetry: it looks the same turned half way round.
4Why does a half butterfly look whole in the mirror?
The mirror image is the mirror reverse of the half, which is exactly the missing half of a symmetrical shape.
Take it further
Set the mirrors at 72 degrees and place a line segment between them to see a regular pentagon appear.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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