Giant Kaleidoscope

Tasks
Step into the kaleidoscope to see infinite reflections of yourself.
Do any of the reflections look odd? What happens if you wave with your right hand?
Is there a pattern to the rotations and reflections?
Maths

The first mirror creates a reflection, the second mirror creates reflections-of-reflection, and the third mirror creates infinitely many reflections. When the mirrors are placed at 60˚ they create hexagonal patterns.

We are used to seeing ourselves reflected in a mirror, but some of your reflections here may look strange. That’s because half of the images are reflections, and half of the images are reflections-of-reflections, which create a rotation.

The set of infinite reflections will look like this:
History

Rotations and reflections have been studied for thousands of years. However, the kaleidoscope was invented in 1817 by Scottish scientist Sir David Brewster. Brewster discovered the beautiful patterns while investigating light polarisation, and spent some time perfecting the kaleidoscope to make beautiful patterns, including adding coloured beads, and to place the three mirrors in a tube with a lens at the end. Soon, the kaleidoscope became a sensation, selling an estimated two hundred thousand kaleidoscopes in London and Paris in just three months.
People
Giambattista della Porta 1535 – 1615
Giambattista della Porta was an Italian scholar and playwright. He is famous for his work in codes and secret messages, and claims to have invented the telescope. In 1558, he wrote a popular science book called Magia Naturalis (Natural Magic) where he described the effect of two hinged mirrors.
David Brewster 1781 – 1768
David Brewster was a Scottish scientist and inventor. Brewster studied polarised light and was a pioneer in photography. Brewster invented a new type of camera, a way to view images in 3D, and the kaleidoscope.

Applications

Mirrors and lenses are used in a variety of scientific instruments and everyday objects. These include telescopes, microscopes, cameras and fibre optic cables. These instruments magnify images or transmit light through a series of reflections.
Maths at Home

Make a kaleidoscope at home with these instructions.