The blue bead appears on the right-hand edge in the fourth set of reflections (8 o'clock and 4 o'clock). The third set of reflections (9 o'clock and 3 o'clock) shows the blue bead back on the left-hand edge. The reflections at 10 o'clock and 2 o'clock are the second set of reflections the blue bead appears on the right-hand edges of these wedges. Given the way light hits a mirror and reflects away at the same angle, a blue bead placed at the right-hand edge of the original wedge would appear in the same position on the left-hand edges of the first set of reflections. If the original wedge is at the very top (at 12 o'clock on a clock face), the reflections on its right and left (11 o'clock and 1 o'clock) are the first reflections of the original image. In a two-mirror kaleidoscope, a 30-degree wedge has 11 reflections. The more precisely the mirrors or reflective surfaces are joined together, the more precise the resulting symmetrical images will be. In a kaleidoscope, each repeated image is symmetrical in relation to the image beside it. Commonly, you'd say that they're mirror images of each other.

If you draw a line down the center of a symmetrical object, the halves on either side of the line are the same. This is due in part to the principle of symmetry. Even the simplest collection of ordinary buttons, beads or glass pieces is transformed into an intricate and beautiful design when a kaleidoscope does its work.

The smaller the slice, the more times it appears.įortunately, the image in the average kaleidoscope is far more interesting than pizza. If the slice is half that size - a 45-degree angle - it's reflected eight times in the image. In a kaleidoscope with two mirrors, that pizza slice appears four times in the image at the end of the kaleidoscope. For example, if your slice is one-fourth of the whole pizza, the angle is 90 degrees. The size of the angle determines how many times that slice is reflected. The fatter the wedge, the wider the angle is at its point the thinner the wedge, the smaller the angle. Each pizza slice or triangle in the kaleidoscope is a portion of that. However, if you put that slice of pizza between two angled mirrors, what you'd see would look almost like a whole pizza made up of numerous reflections of that one slice, side by side.īasic geometry tells us that a circle, like a complete pizza, is 360 degrees around. A single slice might represent the objects that are displayed in the vee-shaped or triangular area of a kaleidoscope.

Image of kaleidoscope patterns