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30 November 2001

The Optical Toy of Sir Brewster

by David Weiller

Every student of optics knows Sir David Brewster (1781 to 1868) for his contributions to polarized light, particularly through the study of the Brewster’s angle. But did you know that Brewster also invented the kaleidoscope? Let us consider how it happened.

David Brewster was born in a small village of Scotland, on December 11, 1781. By the age he was ten and under the influence of a local craftsman, he had built a telescope.

When he was twelve, he enrolled at the University of Edinburgh. By the age of nineteen (1800) Brewster received an M.A., and made his first discovery in optics. Within ten years, his results were regularly published in journals.

In 1814, he studied the polarization of light by successive reflections between glass plates. After publication of his work, he won the Copley Medal from the Society. During his experimental work, Brewster noted "the circular arrangement of images of a candle round a center, and the multiplication of the sector formed by the extremities of the plates of glasses" used as mirrors.

One year later (1815), Brewster discovered the development of complementary colors by successive reflections of polarized light. Once again, he noted the multiple images, which this time were colored. In a letter to the Frenchman J. B. Biot (1774 to 1862), he wrote that by holding two mirrors "inclined at a very small angle, the two series of reflected images appeared at once in the form of two curves; and that the succession of splendid colors formed a phenomenon which I had no doubt would be considered, by every person who saw it to advantages, as the most beautiful in optics."

Like many scientist of all time, the beauty created distracted Brewster researches on the nature of light. This is how the idea of the kaleidoscope came to his mind. In studying the action of fluids on polarized lights, Brewster used a triangular reflective shape. He noted once again the multiple reflections that were this time with greater symmetry.

Brewster next conceived an instrument that attained perfect symmetry, and he displayed it to entertain some of his colleagues at the Royal Society of Edinburgh. Thinking that a moving element would enhance the effect, he used a convex lens to image distant objects onto the end of the reflector. This became the final form of his kaleidoscope.

Brewster decided to patent the kaleidoscope. However, he had prematurely exhibited it to London opticians before obtaining the patent, and his idea was pirated. In only three month, 200,000 kaleidoscopes were sold in London and Paris. However, Brewster, a Scotsman, was not particularly perturbed. He was more concerned by sharing the knowledge and beauty of this optical instrument. And certainly, we are struck more forcibly by his substantial contribution than by this toy.

The maths

When rectangular mirrors that are the same size are arranged with an angle, rays of light from an object form multiple images due to reflections from the mirrors.

For example, a 90° configuration gives 1 object and 3 images:

Similarly, two mirrors oriented at 60° generate 5 images.

When the tree mirrors are arranged in an equilateral triangle, the possibilities become even more interesting.

Build a kaleidoscope

Place three mirrors as shown. Hold the kaleidoscope above small objects on a white cardboard and look through it.

Try to place a convex lens at the end of the kaleidoscope to image distance object. Be sure that the lens has a focal of 3 to 4 times less than the mirrors length.

Find out more on optics at the author’s On-line Optical Library: www.optics2001.com

Your comments and input are welcome. Write to: David Weiller at optics2001@optics2001.com

Copyright (C) 2001 David Weiller. All rights reserved.