---
title: "Mirrors and Reflection"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 32
exercises: 11
source: https://one-course.com/books/physics/1/en/chapter/32-mirrors-and-reflection
---

# Chapter 32 — Mirrors and Reflection

[Light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source), we proved, never bends around corners — and yet every morning a copy of you looks out of the bathroom wall, and last year we promised a trick to see around corners after all. The trick is not to bend the road but to *fold* it. Everything folds at one remarkable surface: the [mirror](#def-g5-mirrors-reflection-reflection).

## 32.1 The bounce

**Definition 32.1 (Reflection).**

When [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) strikes a surface and springs back instead of passing through or dying there, we call it *reflection*: the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) is reflected. A *mirror* is a surface so smooth that it reflects [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) in a perfectly orderly way — polished metal behind glass, still water, a gleaming spoon.

**Proposition 32.2 (The bounce rule).**

A ray of [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) bounces off a [mirror](#def-g5-mirrors-reflection-reflection) the way a perfect ball bounces off a wall: it leaves exactly as steeply as it arrived, on the other side. Straight in — straight back out. Slanting in — slanting out at the matching slant. The two angles, arriving and leaving, are always equal.

![The bounce rule: the leaving ray mirrors the arriving one — equal angles either side of the upright.](https://one-course.com/images/onecourse/chapters/physics-1/g5-mirrors-reflection/fig-f11bbee7bff4.svg)

*The bounce rule: the leaving ray [mirrors](#def-g5-mirrors-reflection-reflection) the arriving one — equal angles either side of the upright.*

**Example 32.3 (Aiming a bounce).**

Because the bounce is so orderly, it can be *aimed*: with a small [mirror](#def-g5-mirrors-reflection-reflection) in the sunshine you can throw a spot of [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) onto any wall you choose — tilt the [mirror](#def-g5-mirrors-reflection-reflection), the spot obeys. Sailors and hikers in trouble use exactly this: a flashed [mirror](#def-g5-mirrors-reflection-reflection) aimed at a far-off ship or helicopter is a signal visible for many kilometres, powered entirely by the Sun.

**Example 32.4 (Why walls are not mirrors).**

A white wall reflects plenty of [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) — the room would be gloomy otherwise — so why does it show no [image](#prop-g5-mirrors-reflection-image)? Up close, its surface is a landscape of tiny bumps: each arriving ray obeys the bounce rule on its own little slope, and the orderly army of rays is scattered to all directions. A [mirror](#def-g5-mirrors-reflection-reflection)’s polish keeps the slopes flat, the army stays in step, and the picture survives the bounce. Order, not shininess alone, is what makes an [image](#prop-g5-mirrors-reflection-image).

![A still lake is a mirror lying down: every ray bounces by the same rule, and the mountain appears again, upside down and exact.](https://one-course.com/images/onecourse/chapters/physics-1/g5-mirrors-reflection/img-1901b9abc21d.jpg)

*A still lake is a [mirror](#def-g5-mirrors-reflection-reflection) lying down: every ray bounces by the same rule, and the mountain appears again, upside down and exact.*

## 32.2 The person behind the glass

**Proposition 32.5 (The image rule).**

A flat [mirror](#def-g5-mirrors-reflection-reflection) shows every object as an *image* standing *behind* the glass, exactly as far behind as the object stands in front, matching it in size, point for point. Step back, and your [image](#prop-g5-mirrors-reflection-image) steps back too; the mirror-world is a faithful, folded copy of ours.

![The image rule: the eye receives a bounced ray, but traces it straight back — to a candle seemingly standing behind the glass, as far back as the real one stands in front.](https://one-course.com/images/onecourse/chapters/physics-1/g5-mirrors-reflection/fig-74674b409eb7.svg)

*The [image](#prop-g5-mirrors-reflection-image) rule: the eye receives a bounced ray, but traces it straight back — to a candle seemingly standing behind the glass, as far back as the real one stands in front.*

**Example 32.6 (Why the image lives behind).**

Your eye is a simple soul: it assumes every ray traveled straight. The bounced ray truly comes from the candle by way of the [mirror](#def-g5-mirrors-reflection-reflection) — but the eye prolongs it *backward through the glass*, to where the ray seems to have started. All the bounced rays agree on that phantom starting point: one candle’s worth of rays, one crisp phantom candle. Nothing stands behind the wall, of course — the [image](#prop-g5-mirrors-reflection-image) is [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s most convincing illusion.

**Example 32.7 (The swapped world).**

Hold a page of writing to the [mirror](#def-g5-mirrors-reflection-reflection): the letters come back reversed, left and right exchanged. That is why the word AMBULANCE is painted mirror-reversed on the front of ambulances: drivers ahead, glancing into their rear-view [mirrors](#def-g5-mirrors-reflection-reflection), see it swing back to plain reading — and pull aside. Two [mirrors](#def-g5-mirrors-reflection-reflection) can undo the swap: a double bounce flips the flip.

## 32.3 Folding the road on purpose

**Method 32.8 (Building a periscope).**

The promised corner-looker, delivered:

1. take a tall, narrow box; cut a window near the top of one face and another near the bottom of the opposite face;
2. fix a small [mirror](#def-g5-mirrors-reflection-reflection) inside behind each window, each tilted at half a right angle, the two tilts parallel to each other;
3. aim the top window over the wall (or around the corner), and look into the bottom window.

The [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s road folds twice: down the box between the [mirrors](#def-g5-mirrors-reflection-reflection), then out into your eye. Submarine crews watch the waves through exactly this — built long and watertight.

![Inside the periscope: two parallel tilted mirrors fold the light’s road twice — over the wall and into your eye.](https://one-course.com/images/onecourse/chapters/physics-1/g5-mirrors-reflection/fig-5a7a548e6441.svg)

*Inside the periscope: two parallel tilted [mirrors](#def-g5-mirrors-reflection-reflection) fold the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s road twice — over the wall and into your eye.*

**Remark 32.9 (Fun-house spoons).**

Look into the bowl of a polished spoon: you hang upside down. Turn it over: you are right side up again, but stretched. Curved [mirrors](#def-g5-mirrors-reflection-reflection) still obey the bounce rule at every point — but their slopes turn with the curve, so the orderly bounces gather or spread, and [images](#prop-g5-mirrors-reflection-image) shrink, grow, or somersault. Curved [mirrors](#def-g5-mirrors-reflection-reflection) focus [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) too: a curved dish of sunlight can cook a pot — remember the solar cookers of the [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) chapter. Their precise laws belong to a later year; the spoon is their honest preview.

## 32.4 Exercises

**Exercise 32.1 ★.**

State the bounce rule. What does a ray arriving straight-on do?

**Solution of Exercise 32.1.**

[Light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) bounces off a [mirror](#def-g5-mirrors-reflection-reflection) leaving exactly as steeply as it arrived, on the other side — equal angles. A ray arriving straight-on bounces straight back along its own road.

**Exercise 32.2 ★.**

A white wall reflects lots of [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source). Why does it show no [image](#prop-g5-mirrors-reflection-image), while the polished [mirror](#def-g5-mirrors-reflection-reflection) does?

**Solution of Exercise 32.2.**

The wall’s surface is a landscape of tiny bumps: each ray obeys the bounce rule on its own little slope, so the rays scatter every which way and the picture dissolves. The [mirror](#def-g5-mirrors-reflection-reflection)’s polish keeps all the bounces in step — order preserved, [image](#prop-g5-mirrors-reflection-image) preserved.

**Exercise 32.3 ★.**

You stand $2\,\mathrm{m}$ in front of a flat [mirror](#def-g5-mirrors-reflection-reflection). Where is your [image](#prop-g5-mirrors-reflection-image), and how far is it from you?

**Solution of Exercise 32.3.**

Behind the glass, $2\,\mathrm{m}$ deep — so $2 + 2 = 4\,\mathrm{m}$ from you.

**Exercise 32.4 ★.**

You walk toward your [mirror](#def-g5-mirrors-reflection-reflection) [image](#prop-g5-mirrors-reflection-image) at a slow step. What does the [image](#prop-g5-mirrors-reflection-image) do, and how fast does the gap between you close?

**Solution of Exercise 32.4.**

The [image](#prop-g5-mirrors-reflection-image) walks toward you at the same slow step, staying exactly as deep behind the glass as you are in front. The gap closes at double your speed — one step of yours plus one of the [image](#prop-g5-mirrors-reflection-image)’s.

**Exercise 32.5 ★.**

Why is AMBULANCE painted backward on the front of ambulances? For whom does it read correctly, and through what?

**Solution of Exercise 32.5.**

A [mirror](#def-g5-mirrors-reflection-reflection) swaps left and right, and a second [mirror](#def-g5-mirrors-reflection-reflection) swaps them back. The word is pre-reversed so that drivers ahead, reading it *through their rear-view [mirror](#def-g5-mirrors-reflection-reflection)*, see it swapped once more — back to plain AMBULANCE.

**Exercise 32.6 ★.**

In the periscope, how many times does the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s road fold, and what does each fold? At what tilt do the [mirrors](#def-g5-mirrors-reflection-reflection) stand?

**Solution of Exercise 32.6.**

Twice — once at each tilted [mirror](#def-g5-mirrors-reflection-reflection). The top [mirror](#def-g5-mirrors-reflection-reflection) folds the scene’s [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) downward through the box; the bottom one folds it out into the eye. Both stand at half a right angle, tilted parallel.

**Exercise 32.7 ★.**

How can a hiker with a pocket [mirror](#def-g5-mirrors-reflection-reflection) signal a far-away helicopter? Which two chapter ideas are at work — name the rule that aims the flash and the store that powers it.

**Solution of Exercise 32.7.**

Tilt the [mirror](#def-g5-mirrors-reflection-reflection) until the bounced sunbeam lands on the target — the bounce rule makes the flash aimable; the Sun is the [energy store](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-store), delivering the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) for free. A pocket-sized flash can be seen for kilometres.

**Exercise 32.8 ★.**

Still water mirrors the mountains; [wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind) ruffles the lake and the picture shatters into glitter. Explain both states with [Example 32.4](#ex-g5-mirrors-reflection-walls).

**Solution of Exercise 32.8.**

Still water is one smooth surface: bounces stay in step, and the mountains’ picture survives — a [mirror](#def-g5-mirrors-reflection-reflection). [Wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind) breaks the surface into countless tilted patches; each patch bounces by the rule on its own slant, the army falls out of step, and the [image](#prop-g5-mirrors-reflection-image) shatters into dancing glitter.

**Exercise 32.9 ★★.**

The eye “prolongs rays backward”. Use this to explain why your [image](#prop-g5-mirrors-reflection-image) stands *behind* the wall the [mirror](#def-g5-mirrors-reflection-reflection) hangs on — in a place where certainly nobody stands. What do all the bounced rays from your nose agree about?

**Solution of Exercise 32.9.**

Each bounced ray reaches the eye from the [mirror](#def-g5-mirrors-reflection-reflection), but the eye prolongs it straight backward, through the glass. All the rays bounced from your nose, prolonged backward, cross at one and the same spot behind the wall — so the eye builds a phantom nose there, and phantom point by phantom point, a whole phantom you. Agreement among rays is what makes the illusion crisp.

**Exercise 32.10 ★★.**

A shop wants a customer at the door to see around a blind corner into the aisle. One flat [mirror](#def-g5-mirrors-reflection-reflection) must be mounted where the two corridors meet. How should it be tilted, and why does the same mounting let the aisle see the door? ([Light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s roads work both ways.)

**Solution of Exercise 32.10.**

Mount it at half a right angle to both corridors (tilted across the corner, like the periscope’s [mirrors](#def-g5-mirrors-reflection-reflection)). A ray from the aisle folds at the [mirror](#def-g5-mirrors-reflection-reflection) and runs to the door — and since [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s roads work both ways, a ray from the door folds along the same path back into the aisle: each end sees the other in the same glass.

**Exercise 32.11 ★★.**

[Mirror](#def-g5-mirrors-reflection-reflection) writing comes back reversed; a double bounce “flips the flip”. Explain why the periscope of [Method 32.8](#met-g5-mirrors-reflection-periscope), with its two [mirrors](#def-g5-mirrors-reflection-reflection), shows the scene the right way around and not mirror-reversed.

**Solution of Exercise 32.11.**

One bounce reverses left and right; the periscope bounces the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) twice, and the second [mirror](#def-g5-mirrors-reflection-reflection) undoes the first [mirror](#def-g5-mirrors-reflection-reflection)’s swap — the flip is flipped back, and the scene arrives the right way around.