Kaleidoscope

Choose the mirror angle first, because it fixes everything else. 60° gives six sectors and a clean hexagonal pattern; 45° gives eight; 30° gives twelve and a dense, busy image.

Cut three strips of mirror or mirrored acrylic 200 x 40 mm. Three strips taped into an equilateral triangle give exactly 60° at every joint with no measuring at all.

Take the sharp edges off every strip with fine paper. Glass mirror cuts skin; acrylic mirror does not, which is why it is the better choice for a first build and for young makers.

Lay the three strips side by side reflective-side down, tape the seams, then fold them into a triangle and tape the last joint. The mirrored faces must all point inward.

Sight down the tube. A gap at any seam prints a black line right through the pattern and no amount of decoration hides it.

Slide the triangle into a cardboard or plastic tube of matching length and pack any slack with paper so it cannot rotate or rattle.

Cap one end with card and pierce a 5 mm hole centred on the mirror triangle. Off-centre and the sectors come out uneven.

Make a shallow chamber at the far end from two clear discs about 10 mm apart. The near disc must be clear; the far one is frosted to diffuse the light.

Put in a few small coloured beads, glass fragments or snips of coloured film — no more than a third full. An overfilled cell jams and the pattern stops changing.

Look through and count the repeated images around the circle. With a 60° triangle you should count six. Divide 360 by your angle and confirm the number matches — this is the measurement the whole build exists for.

Make another with two mirrors at 45° and a black card third side. Count again: eight sectors. Two data points prove the rule rather than illustrating it.

Set the mirrors to 50° and look. The pattern no longer closes — the last sector overlaps the first and the symmetry breaks. Only angles that divide 360 exactly give a clean figure, and seeing the failure teaches more than the success.

Point it at a window, then at a lamp, then at a white wall. The frosted end is doing the work: even, diffuse light behind the objects is what makes the colours read.

Cover the outside and make the object cell rotate freely against the body. A cell that turns under a fingertip is the difference between a demonstration and a toy someone will actually use.

Brewster, 1817. The Scottish physicist David Brewster — better known for the polarisation law that carries his name — conceived the kaleidoscope around 1816 while working on light and patented it in 1817. It was a scientific instrument in intent and a toy within months.

He wrote down which angles look best. The patent names 18°, 20° and 22.5° as producing the most pleasing effect. Those angles give 20, 18 and 16 sectors respectively — dense, intricate figures rather than the simple six of a 60° triangle. It is an unusual document: an inventor specifying the aesthetics of his device alongside its geometry.

The arithmetic. Two mirrors at an angle θ produce 360/θ images including the original, because each reflection rotates the image by 2θ around the joint until the images come back round to the start. When 360/θ is a whole number the figure closes seamlessly; when it is not, the last sector overlaps and the symmetry breaks visibly. This is the same reason floor tilings work with triangles, squares and hexagons and not with pentagons.

The patent did him little good. The kaleidoscope was copied immediately and sold in enormous numbers across Britain and France, and Brewster made very little from an invention that was a genuine craze. It is a recurring pattern in this period: patenting an idea that is trivially easy to reproduce protects almost nothing.

Why it stayed. Most optical toys of the era — thaumatropes, phenakistoscopes, zoetropes — were absorbed by cinema and disappeared as objects. The kaleidoscope had no successor technology to be swallowed by, so it is still made and sold in essentially Brewster's form, two centuries on.