Polarized Light Kaleidoscopes: Colour Without Coloured Glass

4 days ago

6 min read

By Rocco (Roi) Ramon - licensed architect, founder of Studio Yabaye

A polarized light kaleidoscope contains no coloured glass, no dye and no pigment. Its object cell holds clear material only: strips of transparent film, tape, mica or stressed plastic. Outside the instrument these pieces look colourless. Between two polarizing filters they show saturated colour, and the colours change when one filter is turned.

This article explains how the two-filter arrangement works, why a clear material produces colour, why a 90 degree turn of one filter swaps every colour for its complement, and how the method connects to Sir David Brewster.

What polarized light is

Light is a transverse wave. Its electric field vibrates at right angles to the direction of travel. In light from the sun or a lamp, the direction of that vibration changes at random. This is unpolarized light.

In linearly polarized light the field vibrates in one plane only. A polarizing filter produces it: the filter passes the part of the vibration that lies along its transmission axis and absorbs the part at right angles to it.

Two consequences matter for the instrument:

Light loss. An ideal polarizer passes half of the unpolarized light that reaches it. Real sheet filters pass less than half.
Extinction. A second polarizer passes a fraction that depends on the angle between the two axes. This is Malus's law: transmitted intensity is proportional to the square of the cosine of that angle. With the axes at 90 degrees, called crossed polarizers, two ideal filters pass nothing.

The arrangement: two filters and a clear layer between them

A polarized light kaleidoscope adds three elements to the light path, in this order:

Polarizer. The first filter, between the light source and the objects. It turns the incoming light into linearly polarized light.
Birefringent objects. Clear pieces in the object cell: stretched plastic film, cellophane tape, thin mica sheet, or clear plastic carrying internal stress.
Analyzer. The second filter, between the objects and the eye. It is the same kind of filter as the first.

The mirror system does the same work as in any kaleidoscope: it repeats the view of the object cell around the axis. The mirrors do not create the colour. For the mirror optics, see how a kaleidoscope works and mirror angle and number of points.

The order matters. If both filters sit on the same side of the objects, no colour appears. For other object-cell types, see types of kaleidoscopes.

Why a clear material shows colour

A birefringent material has two refractive indices. Light polarized along one direction in the material, the slow axis, travels more slowly than light polarized along the perpendicular direction, the fast axis. Stretching a plastic film during manufacture produces this property. So does mechanical stress in a clear plastic.

Splitting. Polarized light enters the film. Unless its plane lies exactly along the fast or the slow axis, it divides into two components, one on each axis.

Delay. The two components travel at different speeds and leave the film out of step. The path difference, called retardation, equals the film thickness multiplied by the difference between the two refractive indices.

Dependence on wavelength. A given retardation is a different fraction of a wave for each wavelength. A retardation of 550 nanometres is one full wave for green light at 550 nanometres, about 0.85 of a wave for red light at 650 nanometres and about 1.2 waves for blue light at 450 nanometres. Each wavelength leaves the film in a different polarization state.

Selection. The analyzer passes only the part of each wavelength that lies along its axis. White light goes in. A spectrum with parts removed comes out, and the eye reads that as a colour.

The result depends on two variables:

Thickness. Two layers of the same tape give twice the retardation of one layer, and a different colour.
Orientation. The colour is strongest when the film axes lie at 45 degrees to the polarizer axis. When a film axis is parallel to the polarizer axis, the light is not split and no colour appears.

Dichroic glass also takes its colour from interference, by a different mechanism: see dichroic glass in kaleidoscopes.

Why turning one filter swaps each colour for its complement

The analyzer sorts each wavelength into two parts: the part along its axis, which it passes, and the part across its axis, which it absorbs.

Turn the analyzer by 90 degrees and the two parts change places. For every wavelength, the intensity seen in the first position plus the intensity seen in the second equals the full intensity that reached the analyzer.

Two colours that add up to white are complementary. A region that looks green in one position looks magenta in the other. The clear background is dark with the filters crossed and bright with the filters parallel.

The historical link: Brewster and polarization

The kaleidoscope came out of polarization research. Brewster states this in the history that opens his book "The Kaleidoscope: Its History, Theory, and Construction". The first idea of the instrument, he writes, came to him in 1814, during "a series of experiments on the polarization of light by successive reflexions between plates of glass". Those experiments were published in the Philosophical Transactions for 1815, and the Royal Society awarded him the Copley Medal for them.

He records a second date in the same passage. On 7 February 1815 he observed complementary colours produced by successive reflections of polarized light between two plates of gold and silver. The patent for the kaleidoscope was granted in 1817.

Brewster's other results in optics include two that apply here:

Brewster's angle. Light reflected from a transparent surface at one specific angle of incidence is completely polarized. The tangent of that angle equals the refractive index of the material. For glass with an index of 1.5 the angle is about 56 degrees.
Stress birefringence. He showed that glass becomes birefringent under mechanical compression and shows colours in polarized light. This is the basis of photoelasticity, the method of reading stress in a transparent model from its colour fringes. The Royal Society awarded him the Rumford Medal in 1818, for discoveries relating to the polarization of light, and a Royal Medal in 1830.

The book also contains a chapter on the construction of kaleidoscopes "which combine the colours and forms produced by polarized light" (Chapter XVI). For the wider timeline, see history of the kaleidoscope.

Limits of the method

Light loss. The first filter removes at least half of the incoming light, the second removes more, and each mirror reflection loses a further part. The image is dimmer than in an instrument with the same mirrors and no filters, so it needs a bright, direct source.
Sensitivity to the source. Light from a clear blue sky is partly polarized. With such a source, brightness and colours change as the tube is turned.

Checklist: reading a polarized kaleidoscope

The objects are clear when seen outside the light path.
Turning one filter changes all colours at once.
Two filter positions 90 degrees apart give complementary colours.
With crossed filters the empty background is dark.

FAQ

What is a polarized light kaleidoscope?

It is a kaleidoscope in which the colour comes from polarization and not from coloured objects. The object cell holds clear birefringent pieces placed between two polarizing filters. The mirror system repeats the view as usual. The pieces look colourless outside the instrument and coloured inside it, on a dark or bright background.

How does a polarized kaleidoscope produce colour from clear material?

The first filter polarizes the light. The clear birefringent piece splits it into two components that travel at different speeds and leave out of step. The delay is a different fraction of a wave for each wavelength, so the second filter passes some wavelengths and blocks others. The remaining light is coloured.

Why do the colours change when one filter is rotated?

The second filter passes the part of each wavelength lying along its axis and absorbs the part across it. A 90 degree turn exchanges the two parts. Each colour is replaced by its complement, for example green by magenta, and the background changes between dark and bright at the same time.

What materials work as objects in a polarized kaleidoscope?

Clear birefringent materials: stretched plastic film, cellophane tape, thin mica sheet, and clear plastic with internal stress from moulding or bending. The colour depends on the thickness of the layer and on its orientation relative to the filters. Two overlapping layers of the same tape show a different colour from one layer.

What did David Brewster have to do with polarized light?

Brewster received the Copley Medal in 1815 for experiments on polarization by reflection and the Rumford Medal in 1818. The relation between polarizing angle and refractive index carries his name, and he showed that stressed glass becomes birefringent. He wrote that the first idea of the kaleidoscope came in 1814 during those experiments.

Why is a polarized kaleidoscope dimmer than one with coloured glass?

An ideal polarizing filter passes half of the unpolarized light that reaches it, and real sheet filters pass less. The second filter removes more, depending on wavelength. The mirror reflections then reduce the light further. The instrument therefore needs a bright, direct source to give a readable image.

About Studio Yabaye

I build the Studio Yabaye kaleidoscopes and teleidoscopes with front-surface mirror systems in several configurations, each in a brass tube, cut, fitted and hand-finished in the studio. Each object wheel is poured and composed by hand, so no two pieces are alike. Kaleidoscopes need direct, preferably strong light. The studio is based in Israel and ships worldwide. The current range is at all products, and questions can be sent through the contact page.