📐

SEC 2027 · G3 SEC 4 Pure Physics

Sec 4 Pure Physics
Visual Notes

Pictures first. Formulas boxed. Every exam keyword highlighted.

HOW TO STUDY WITH THIS

Read the 💡 box
the whole topic in 1 line

Study the diagram
cover it, redraw it

Learn the yellow
formulas & keywords

Redo the worked example
without looking

THE CHAPTERS

🌊

CH 1

General Properties of Waves

v = fλ

📡

CH 2

Electromagnetic Spectrum

order

💡

CH 3

Light: Reflection & Refraction

laws

🔍

CH 4

Lenses

converging lens

✨

CH 5

Static Electricity

charging

🔋

CH 6

Charge & Current Electricity

Q = It

🔀

CH 7

D.C. Circuits

series

🔌

CH 8

Practical Electricity

power

🧲

CH 9

Magnetism & Electromagnetism

magnetic fields

🔁

CH 10

Electromagnetic Induction

Faraday

☢️

CH 11

Radioactivity

α β γ

📌 NOTESchools split Sec 3 / Sec 4 physics differently — check the other year if a chapter is missing.

🖨 PRINTCtrl+P → Save as PDF · Scale 100% · Margins None · Background graphics ON

Sec 4 Pure Physics · SEC K323

🌊

General Properties of Waves

v = fλ, transverse & longitudinal, sound

BIG IDEAWaves transfer energy without transferring matter. v = fλ · f = 1 ÷ T

crest-to-crest = wavelength; centre to crest = amplitude

Term	Meaning
amplitude A	max displacement from rest
wavelength λ	distance between successive crests
frequency f	waves per second (Hz)
period T	time for one wave (s)
wavefront	line joining points in phase (crests)

Transverse	Longitudinal
vibration ⟂ direction of travel	vibration ∥ direction of travel
crests & troughs	compressions & rarefactions
light, water, EM waves	sound

🔊 Sound

needs a medium (not in vacuum) · fastest in solids · loudness ↑ with amplitude · pitch ↑ with frequency · human range 20 Hz–20 kHz

Echo

distance = (speed × time) ÷ 2 — sound goes there and back
ultrasound (> 20 kHz): pre-natal scans, sonar, finding cracks in metal

🔎 WHY IT WORKSWhy v = fλ: in one period T, the wave moves forward exactly one wavelength. So speed = λ ÷ T = fλ.

🧠 Worked example — follow the thinking

A boy claps 170 m from a wall and hears the echo 1.0 s later. Find the speed of sound.

Step	Why I do this
Total distance = 2 × 170 = 340 m	💭 Sound travels to the wall AND back.
v = 340 ÷ 1.0 = 340 m/s	💭 speed = distance ÷ time.

Sec 4 Pure Physics · SEC K323

📡

Electromagnetic Spectrum

order, uses, hazards

BIG IDEAAll EM waves are transverse, travel at 3.0 × 10⁸ m/s in vacuum and need no medium.

"Raging Martians Invaded Venus Using X-ray Guns"

Wave	Use	Hazard
radio	radio/TV broadcasting	—
microwave	cooking, mobile phones, satellites	internal heating of tissue
infrared	remote controls, thermal imaging, toasters	skin burns
visible	seeing, optical fibres, photography	eye damage (lasers)
ultraviolet	sterilising, detecting forged notes	sunburn, skin cancer
X-ray	medical images, airport security	ionising → cell damage, cancer
gamma	killing cancer cells, sterilising food	ionising → cancer, mutation

🔎 WHY IT WORKSWhy higher frequency is more dangerous: high-frequency EM waves carry more energy per "packet", enough to ionise atoms in cells and damage DNA. Low-frequency waves mainly just heat.

🧠 Worked example — follow the thinking

A radio station broadcasts at 100 MHz. Find the wavelength.

Step	Why I do this
v = 3.0 × 10⁸ m/s	💭 All EM waves have this speed.
λ = v ÷ f = 3.0 × 10⁸ ÷ 100 × 10⁶	💭 Rearrange v = fλ; M = 10⁶.
λ = 3.0 m	💭

Sec 4 Pure Physics · SEC K323

💡

Light: Reflection & Refraction

laws, refractive index, total internal reflection

BIG IDEAReflection: i = r. Refraction: n = sin i ÷ sin r = c ÷ v. Light bends towards the normal entering a denser medium.

angles from the normal

Laws

reflection: i = r; incident ray, reflected ray and normal in the same plane
refraction: light changes speed → changes direction
plane-mirror image: same size, upright, laterally inverted, virtual, same distance behind

Refractive index n

n = speed in vacuum ÷ speed in medium
glass n ≈ 1.5 → light at 2 × 10⁸ m/s in glass
no bending if ray enters along the normal

Everyday

pool looks shallower · straw looks bent · diamonds sparkle (TIR)

🔎 WHY IT WORKSWhy a pool looks shallower: light from the bottom bends away from the normal as it leaves water. Your brain traces the ray back in a straight line, so the bottom seems higher than it is.

🧠 Worked example — follow the thinking

Light hits glass (n = 1.5) at i = 40°. Find r.

Step	Why I do this
sin r = sin 40° ÷ 1.5	💭 n = sin i ÷ sin r rearranged.
= 0.643 ÷ 1.5 = 0.4285	💭 Calculator in DEGREE mode.
r = sin⁻¹(0.4285) = 25.4°	💭 r < i: bends towards the normal (denser).

🔦 Total internal reflection

only from denser → less dense and when i > critical angle c · sin c = 1 ÷ n · glass: c = sin⁻¹(1/1.5) = 41.8° · uses: optical fibres (communication, endoscopes), prism periscopes

Sec 4 Pure Physics · SEC K323

🔍

Lenses

converging lens, focal length, images, ray diagrams

BIG IDEAA converging (convex) lens bends parallel rays to meet at the focal point F. Focal length f = lens to F.

ray 1: parallel → through F · ray 2: through the optical centre → straight on

Object	Image	Image is	Use
beyond 2F	between F and 2F	real, inverted, diminished	camera, eye
at 2F	at 2F	real, inverted, same size	photocopier (1:1)
between F and 2F	beyond 2F	real, inverted, magnified	projector
at F	at infinity	—	spotlight
inside F	same side as object	virtual, upright, magnified	magnifying glass

Real vs virtual

real: rays actually meet → can be caught on a screen
virtual: rays only seem to come from it

Find f quickly

focus a distant object (window) on a screen → lens-to-screen distance ≈ f

🔎 WHY IT WORKSWhy the rays are chosen: we already know where these special rays go without measuring angles. Two rays from the top of the object are enough — where they meet is the top of the image.

🧠 Worked example — follow the thinking

Object 3 cm tall is 15 cm from a lens, f = 10 cm. Describe the image by ray diagram.

Step	Why I do this
Scale: 1 cm = 5 cm; mark F at 10 cm both sides	💭 Always draw to scale on graph paper.
Ray parallel → through F; ray through centre straight	💭 Two standard rays.
They meet ≈ 30 cm beyond lens, image ≈ 6 cm tall	💭 Measure from the drawing.
Image: real, inverted, magnified	💭 Object between F and 2F → matches the table.

Sec 4 Pure Physics · SEC K323

✨

Static Electricity

charging, induction, electric fields, hazards & uses

BIG IDEARubbing transfers electrons. Like charges repel, unlike attract. Charged objects attract neutral ones by induction.

Charging by rubbing

polythene rubbed with cloth: electrons move onto polythene → polythene −, cloth +
only electrons move, never protons
insulators keep charge; conductors lose it to earth

Charging by induction

bring − rod near a neutral sphere → electrons pushed to far side → earth the far side (electrons flow away) → remove earth → remove rod → sphere left +

electric field lines: out of +, into −

Electric field

region where a charge feels a force · direction = force on a positive test charge

⚠️ Hazards

lightning · sparks when refuelling aircraft/cars (fuel vapour can ignite) → earth the aircraft and tanker · sparks near flammable gas

✅ Uses

electrostatic precipitator: chimney smoke particles charged, attracted to oppositely charged plates · photocopiers · spray painting (even coat)

🔎 WHY IT WORKSWhy a charged comb picks up neutral paper: the comb pushes electrons in the paper away (or pulls them close), so the near side gets the opposite charge. Opposite charge is closer, so attraction beats repulsion.

🧠 Worked example — follow the thinking

Why is an aircraft earthed before refuelling?

Step	Why I do this
Friction (air, fuel flowing) builds up charge	💭 Rubbing transfers electrons.
Charge could cause a spark → ignite fuel vapour	💭 The hazard.
Earthing lets electrons flow safely to ground	💭 No charge build-up → no spark.

Sec 4 Pure Physics · SEC K323

🔋

Charge & Current Electricity

Q = It, e.m.f., p.d., resistance, I–V graphs

BIG IDEAQ = It · V = W ÷ Q · R = V ÷ I. Current = rate of flow of charge.

Quantity	Definition	Unit
charge Q	—	coulomb C
current I	charge per unit time	ampere A
e.m.f. E	work done by source per unit charge to drive charge round the whole circuit	volt V
p.d. V	work done per unit charge across a component	volt V
resistance R	V ÷ I	ohm Ω

Direction

conventional current: + → −
electron flow: − → + (opposite)

Resistance of a wire

R ∝ length (longer → more collisions) · R ∝ 1 ÷ cross-sectional area (thicker → easier) · R = ρL ÷ A · R of metal ↑ when temperature ↑

ohmic conductor: straight line through origin, R constant

filament lamp: curves — R ↑ as it heats

diode: current one way only

🔎 WHY IT WORKSWhy a longer wire has more resistance: electrons collide with more metal ions along a longer path. A thicker wire gives more paths side by side, so the current flows more easily.

🧠 Worked example — follow the thinking

A charge of 120 C flows through a 6 V lamp in 1 minute. Find I, R and the energy transferred.

Step	Why I do this
I = Q ÷ t = 120 ÷ 60 = 2 A	💭 t must be in seconds.
R = V ÷ I = 6 ÷ 2 = 3 Ω	💭 Definition of resistance.
W = QV = 120 × 6 = 720 J	💭 p.d. = energy per unit charge.

Sec 4 Pure Physics · SEC K323

🔀

D.C. Circuits

series, parallel, effective resistance, potential divider

BIG IDEASeries: same current, voltages add, R = R₁ + R₂. Parallel: same p.d., currents add, 1/R = 1/R₁ + 1/R₂.

Symbol	Component
—\|‖—	cell (long line +)
—⊗—	lamp
—▭—	fixed resistor
—▭↗—	variable resistor
—(A)—	ammeter (series)
—(V)—	voltmeter (parallel)
—▭~—	fuse
—▷\|—	diode / LED (arrows out)

Series

I same everywhere
V_total = V₁ + V₂
R_total = R₁ + R₂ (bigger than each)

Parallel

V same across each branch
I_total = I₁ + I₂
R_total smaller than the smallest branch

Potential divider

V_out = R₂ ÷ (R₁ + R₂) × V_in · thermistor (NTC): R ↓ when hotter · LDR: R ↓ in brighter light · used in fire alarms, automatic street lights

🔎 WHY IT WORKSWhy parallel R is smaller: each new branch is an extra path for charge, so more current flows for the same p.d. — and R = V ÷ I gets smaller.

🧠 Worked example — follow the thinking

6 Ω and 3 Ω in parallel, in series with 4 Ω, on a 12 V supply. Find the current from the supply.

Step	Why I do this
Parallel: 1/R = 1/6 + 1/3 = 1/2 → R = 2 Ω	💭 Combine the parallel pair first.
Total R = 2 + 4 = 6 Ω	💭 Then add in series.
I = V ÷ R = 12 ÷ 6 = 2 A	💭 Whole-circuit V = IR.

🧠 Worked example 2

In a potential divider R₁ = 2 kΩ, R₂ = 3 kΩ, V_in = 10 V. Find V across R₂.

Step	Why I do this
V₂ = 3 ÷ (2 + 3) × 10	💭 p.d. splits in the ratio of resistances.
= 6 V	💭 Bigger resistor takes the bigger share.

Sec 4 Pure Physics · SEC K323

🔌

Practical Electricity

power, energy cost, fuses, earthing, plug

BIG IDEAP = VI · E = VIt · cost = kWh × rate. Fuses and switches go on the live wire.

3-pin plug (UK/SG): live = brown, neutral = blue, earth = green/yellow

Safety devices

fuse: thin wire melts if I too large · rating just above normal current (3, 5, 13 A)
circuit breaker: trips, can be reset
earthing: metal case connected to earth — fault current flows to earth, blows fuse
double insulation (⧈): plastic casing, no earth wire needed

Hazards

damaged insulation → shock · overheating of cables (too much current) · damp / wet conditions → water conducts

Why on the live wire?

if the fuse/switch were on neutral, the appliance would still be at high voltage even when off/blown → shock risk

🔎 WHY IT WORKSWhy heating happens: charges collide with ions in the resistor, transferring energy to them — the resistor gets hot. Used in kettles, irons, heaters.

🧠 Worked example — follow the thinking

A 230 V kettle is rated 2.3 kW. Choose a fuse: 3 A, 5 A or 13 A.

Step	Why I do this
I = P ÷ V = 2300 ÷ 230 = 10 A	💭 Normal working current.
Fuse must be slightly higher than 10 A	💭 Too low → blows in normal use; too high → no protection.
Choose 13 A	💭

Sec 4 Pure Physics · SEC K323

🧲

Magnetism & Electromagnetism

magnetic fields, electromagnets, motor effect

BIG IDEAField lines go N → S. A current makes a magnetic field; a current in a field feels a force (Fleming's left-hand rule).

bar magnet field (closer lines = stronger)

Magnets

like poles repel, unlike attract · iron: soft — easily magnetised and loses it (temporary, electromagnets) · steel: hard — permanent magnets · induced magnetism: iron near a magnet becomes a magnet

Fields from currents

straight wire: circles round the wire — right-hand grip rule
solenoid: like a bar magnet; stronger with more turns, more current, iron core
reverse current → field reverses

✋ Fleming's left-hand rule

First finger = Field · seCond = Current · thuMb = Motion (force)
motor: coil in field → turning effect; split-ring commutator reverses current every half turn so it keeps spinning

🔎 WHY IT WORKSWhy a current-carrying wire moves in a field: the wire's own circular field adds to the magnet's field on one side and cancels it on the other. The wire is pushed from the strong-field side to the weak-field side.

🧠 Worked example — follow the thinking

A wire lies flat on the page. Field points to the right →, current flows up the page ↑. Which way is the force?

Step	Why I do this
First finger → field: point it right	💭 Fingers at right angles to each other.
Second finger → current: point it up the page	💭 Twist your LEFT hand to fit.
Thumb now points into the page → force into the page	💭 Thumb = motion. Reverse either I or B → force reverses.

Sec 4 Pure Physics · SEC K323

🔁

Electromagnetic Induction

Faraday, Lenz, a.c. generator, transformers

BIG IDEAChanging magnetic field through a coil induces an e.m.f. (Faraday). The induced current opposes the change (Lenz).

Bigger induced e.m.f. if…

magnet moves faster · stronger magnet · more turns on the coil · no movement → no e.m.f.

Lenz's law

push N pole in → coil end becomes N (repels it) · pull out → end becomes S · you must do work → energy conserved

a.c. generator output: peak when coil is parallel to field

A.C. generator

coil rotated in a field → e.m.f. alternates · uses slip rings + brushes · faster rotation → higher peak AND higher frequency

🔁 Transformer

Vs ÷ Vp = Ns ÷ Np · ideal: VpIp = VsIs · works only with a.c. (needs a changing field) · laminated soft-iron core · step-up for transmission: high V → low I → less I²R heat loss in cables

🔎 WHY IT WORKSWhy transformers need a.c.: a.c. makes the field in the core keep changing, which induces e.m.f. in the secondary. Steady d.c. gives a constant field — no change, no induction.

🧠 Worked example — follow the thinking

A transformer steps 230 V down to 11.5 V. Np = 2000. Find Ns and Ip if Is = 4 A (ideal).

Step	Why I do this
Ns = Np × Vs ÷ Vp = 2000 × 11.5 ÷ 230	💭 Turns ratio = voltage ratio.
Ns = 100 turns	💭
VpIp = VsIs → Ip = 11.5 × 4 ÷ 230	💭 Power in = power out (ideal).
Ip = 0.2 A	💭 Step down V → step up I.

Sec 4 Pure Physics · SEC K323

☢️

Radioactivity

α β γ, half-life, isotopes, fission & fusion

BIG IDEAUnstable nuclei decay randomly and spontaneously, giving out α, β or γ. Half-life = time for half the nuclei to decay.

Nuclide notation

ᴬ_ZX
A = nucleon number (p + n) · Z = proton number
isotopes: same Z, different A (e.g. ¹²C, ¹⁴C)

each half-life halves the activity

	α alpha	β beta (β⁻)	γ gamma
Is	helium nucleus (2p 2n)	fast electron	EM wave
Ionising	strongest	medium	weakest
Stopped by	paper / few cm air	few mm aluminium	thick lead / concrete
Charge	+2	−1	0

Uses

γ: kill cancer cells, sterilise · β: paper thickness control · α: smoke detectors · tracers (short half-life)

Safety

background radiation from rocks, cosmic rays, food · minimise time, maximise distance, use shielding · tongs, lead aprons

Equations & nuclear energy

α decay: A −4, Z −2 · β⁻ decay: A same, Z +1 (n → p + e⁻) · γ: no change · fission: heavy nucleus splits (power stations) · fusion: light nuclei join (Sun)

🔎 WHY IT WORKSWhy we use half-life: we can never say WHEN one nucleus will decay — it is random. But with billions of nuclei, the fraction left after a set time is very predictable.

🧠 Worked example — follow the thinking

A sample has activity 800 Bq; half-life 3 days. Find activity after 12 days.

Step	Why I do this
12 ÷ 3 = 4 half-lives	💭 Count how many half-lives pass.
800 → 400 → 200 → 100 → 50	💭 Halve each time.
Activity = 50 Bq	💭

Sec 4 Pure Physics · SEC K323

Sec 4 Pure PhysicsVisual Notes

General Properties of Waves

Electromagnetic Spectrum

Light: Reflection & Refraction

Lenses

Static Electricity

Charge & Current Electricity

D.C. Circuits

Practical Electricity

Magnetism & Electromagnetism

Electromagnetic Induction

Radioactivity

Sec 4 Pure Physics
Visual Notes