Hall of Mirrors

Why it matters

One mirror gives one twin. Two mirrors facing each other give an infinite corridor. And two mirrors at an angle give EXACTLY as many twins as a formula decides — no more, no less.

The idea in plain words

The image-counting machine. Tap the terms.

n = 360/θ − 1

Mirrors at 90° — how many images of the candle between them?

3 images — try it with two pocket mirrors tonight

• degrees: θ — the angle between the two mirrors — smaller angle, more images
• the limit: parallel mirrors — θ → 0: infinite images, each dimmer — the barber-shop corridor
• the toy: kaleidoscope — two mirrors at 60° making 5-fold symmetric patterns from junk beads
• the tool: periscope — two PARALLEL mirrors at 45° tilts — see over walls (plane-mirror edition)
• n = 360/90 − 1

Predict first

Two mirrors at 60° hold a coin between them. How many images?

n = 360/60 − 1 = 5. Each image becomes an object for the OTHER mirror — reflections of reflections, until the geometry runs out.

• 5 — correct
• 6
• 2 — one per mirror

What you do

Close and open the mirror pair — make exactly 5 images, then exactly 3.

Check yourself

To get MORE images between two mirrors,…

360/θ grows as θ shrinks — at 30° you get 11 twins.

In a barber shop with parallel mirrors, far images look dimmer because…

No mirror is perfect; ~5–10% is lost per bounce, so the corridor fades into the dark.

A kaleidoscope's endless patterns come from…

Loose beads + n = 360/θ − 1 = symmetric art, patented in 1817 and still selling.

• decrease the angle between them — correct
• increase the angle
• use bigger mirrors
• each reflection absorbs a little light — many bounces, much loss — correct
• they are physically farther objects
• your eyes tire
• multiple reflections in two inclined mirrors — correct
• coloured lenses
• a rotating motor