The disk at the end of the tube (drag it round)
What you see through the eyepiece
Two mirrors at 60°: 6 pieces fit round the middle (360° ÷ 60° = 6): the real piece and 5 reflections. The ones farther round are reflections of reflections, bounced from one mirror to the other.
- Mirrors
- 2
- Angle between them
- 60°
- Pieces you see
- 6
What’s happening
A kaleidoscope is a tube lined with mirrors, with colored shapes at the far end. Through the eyepiece you see only one small piece of them directly: the piece between the mirrors, outlined on the disk. Every other piece in the circle is a reflection of it, or a reflection of a reflection, bounced from mirror to mirror. The shapes don’t need to be neat at all: the mirrors make the pattern. Turn the disk and a different piece slides between the mirrors, and the whole pattern changes at once.
Try this
- With two mirrors, find the real piece in the view. Which pieces are mirror images of it, and which are the right way round?
- Make the angle between the two mirrors smaller. How many pieces fit round the middle now?
- Switch to a triangle of mirrors. Does the pattern ever end?
- Why are the pieces far from the middle darker?
- At home: tape two small mirrors together along one edge, like a book, and stand them round a coin. Close the book slowly and count the coins.
Learn more: why the angle matters, endless tubes, and patterns made without mirrors
Two mirrors. Stand two mirrors on their edges, touching, at an angle . Each one reflects the piece between them, each reflects the other’s reflection, and so on, until the copies meet all the way round. They fit round the middle without a gap only when goes into 360° a whole number of times:
So 90° makes 4 pieces, 60° makes 6, 45° makes 8 and 30° makes 12. Half of them are the right way round and half are mirror images, side by side, which is why the pattern always looks folded along its spokes. With an angle that doesn’t fit, say 50°, the last reflections don’t match where they meet, and you see a seam. That’s why a kaleidoscope’s mirrors are fixed at an angle like 60°, never just roughly.
Three or four mirrors. A tube with three mirrors in a triangle has no open side: every reflection is reflected again by another mirror, on and on, so the copies fill the whole view like tiles on a floor. Only a few shapes tile without seams: a triangle with corners of 60°, 60° and 60°, one with 90°, 45° and 45°, one with 90°, 60° and 30°, and a rectangle. The Kaleidoscope exhibit has three tubes, a triangle, a right triangle and a square, so you can compare them.
Why far pieces are darker. A mirror sends back most of the light that hits it, but not all: a good one keeps about 9 parts in 10. A piece far from the middle has bounced many times on its way to your eye, losing a little light at each bounce, so it is dimmer. The same thing happens in the Infinity Well.
Its name. The Scottish scientist David Brewster invented the kaleidoscope in 1816 while studying light. He made up the name from Greek words meaning “observer of beautiful forms”.
- Mandalas, rose windows and tiles: one shape repeated round a middle, the same idea drawn by hand.
- Snowflakes: six-sided because of how water’s molecules fit together, not because of mirrors, but with the same kind of repeating pattern.
- Mirror rooms and lifts: two mirrors facing each other make rows of copies that go on and on, a kaleidoscope with the mirrors at 0°.