The Law of the Bounce
∠i = ∠r — and the 2θ mirror trick
What this lesson covers
Why it matters
Light plays perfect billiards. Every bounce, off every mirror, at every angle, follows one unbreakable rule — and tilting the table bends the shot TWICE as much as you'd guess.
The idea in plain words
The rules of the bounce. Tap them.
∠i = ∠r · all three in one plane
A ray hits a mirror at 35° to the SURFACE. Find i and r.
i = r = 55° — the surface-angle trap, defused
- the convention: the angles — measured from the NORMAL (perpendicular), never from the mirror surface
- mirrors: regular reflection — smooth surfaces: parallel in, parallel out — images form
- paper, walls: irregular (diffuse) — rough surfaces scatter every which way — that's why you can read this page from anywhere
- from the normal: i = 90 − 35 = 55°
- r = i
Predict first
Keep the light fixed and tilt the MIRROR by 15°. The reflected ray swings by…
Tilting the mirror tilts the NORMAL by 15°, changing i by 15° and r by another 15°: the ray turns 2 × 15° = 30°. Instrument-makers live off this doubling.
- 30° — twice the mirror's tilt — correct
- 15° — same as the mirror
- 7.5°
What you do
Tilt the mirror until the beam lands on the sensor — count how little tilt the doubling needs.
Check yourself
A ray hitting a mirror ALONG the normal (i = 0°) reflects…
r = i = 0: retrace. How opticians centre lenses and how cat's-eyes work.
You can read a book from any angle because paper gives…
Rough at the micro-scale, paper sprays each ray differently — no image, but visibility from everywhere.
Both regular AND irregular reflection obey…
Each micro-bounce is lawful; the roughness just aims the normals chaotically.
- straight back on itself — correct
- at 90°
- it doesn't reflect
- irregular (diffuse) reflection — light scatters everywhere — correct
- regular reflection
- no reflection at all
- ∠i = ∠r at every individual point — correct
- different laws entirely
- no laws