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VCE Physics Cheat Sheet
VCE Physics Cheat Sheet — Improved Version
Page 1 — Waves & Light
1) Wave equations
Wave speed: \(v=f\lambda\)
Frequency: \(f=\frac{1}{T}\)
Period: \(T=\frac{1}{f}\)
Key idea: when a wave enters a new medium, frequency stays the same because the source controls it. Speed and wavelength can change.
Example: A wave with \(f=5\,\text{Hz}\) and \(\lambda=2\,\text{m}\) has speed \(v=10\,\text{m/s}\).
2) Transverse vs longitudinal waves
Transverse: vibrations are perpendicular to the direction of travel.
Examples: light, water waves, EM waves.
Longitudinal: vibrations are parallel to the direction of travel.
Example: sound waves in air.
Exam trap: sound is not transverse.
3) Electromagnetic spectrum
Radio → Microwave → Infrared → Visible → Ultraviolet → X-ray → Gamma
Moving right across the spectrum:
frequency increases
energy increases
wavelength decreases
Example memory trick: gamma rays have the highest energy and shortest wavelength.
4) Wien’s law
\[
\lambda_{\max}T = 2.898\times 10^{-3}\,\text{m K}
\]
Hotter objects emit more energy and peak at a shorter wavelength.
Example: if \(T=5800\,\text{K}\), then
\[
\lambda_{\max}=\frac{2.898\times10^{-3}}{5800}\approx 5.0\times10^{-7}\,\text{m}
\]
which is visible light.
5) Refractive index
\[
n=\frac{c}{v}
\]
Higher \(n\) means light travels slower.
Typical values: air \(\approx 1.00\), water \(\approx 1.33\), glass \(\approx 1.5\)
Example: light slows down when it enters glass, so it bends.
6) Snell’s law
\[
n1\sin\theta1 = n2\sin\theta2
\]
Low \(n\) to high \(n\): bends toward the normal.
High \(n\) to low \(n\): bends away from the normal.
Example: air to water → ray bends toward the normal because water has a higher refractive index.
Page 2 — Refraction, TIR & Thermal Physics
1) Total internal reflection (TIR)
TIR happens when:
light goes from higher \(n\) to lower \(n\)
angle of incidence is greater than the critical angle
Critical angle:
\[
\sin\thetac = \frac{n2}{n_1}
\]
Example: optical fibres use TIR to keep light trapped inside the fibre.
2) Dispersion
Different wavelengths refract by different amounts because they have different refractive indices in a material.
Violet bends the most
Red bends the least
Example: a prism spreads white light into a spectrum.
3) Mirages
Hot air near the ground has a lower refractive index. Light bends upward, so the ground can look like it has water on it.
Example: the “water” you see on a hot road is a mirage.
4) Temperature
Temperature is the average kinetic energy of particles.
Convert between Celsius and Kelvin:
\[
T(K)=T(^\circ C)+273.15
\]
Example: \(25^\circ\text{C}=298.15\,\text{K}\)
5) Internal energy
\[
U = \text{KE} + \text{PE}
\]
When temperature changes, average kinetic energy changes.
During a state change, potential energy changes but temperature stays constant.
Example: when ice melts, temperature stays at \(0^\circ\text{C}\) until all the ice has melted.
6) Heat transfer
Conduction: energy transfer by particle collisions, mainly in solids.
Convection: warm fluid rises, cool fluid sinks.
Radiation: infrared EM waves; no medium needed.
Examples:
metal spoon getting hot in soup = conduction
boiling water circulating = convection
feeling the Sun’s heat = radiation
7) Specific heat capacity
\[
Q=mc\Delta T
\]
Example: heating \(2\,\text{kg}\) of water by \(5^\circ\text{C}\):
\[
Q=2\times4200\times5=42000\,\text{J}
\]
8) Latent heat
\[
Q=mL
\]
Used during melting, freezing, boiling, and condensing.
Example: energy is needed to melt ice, but the temperature does not rise while it is melting.
Page 3 — Nuclear Physics
1) Strong nuclear force
Very strong
Very short range
Holds nucleons together in the nucleus
2) Electrostatic force
Protons repel each other
The strong nuclear force must overcome this to keep the nucleus stable
3) Alpha decay
\[
A\rightarrow A-4,\quad Z\rightarrow Z-2
\]
An alpha particle is \(2p+2n\).
Most ionising
Least penetrating
Example: a nucleus losing an alpha particle becomes a different element.
4) Beta minus decay
\[
\text{neutron} \rightarrow \text{proton} + \text{electron}
\]
Mass number \(A\) stays the same
Atomic number \(Z\) increases by 1
Example: beta minus decay happens when a neutron-rich nucleus becomes more stable.
5) Beta plus decay
\[
\text{proton} \rightarrow \text{neutron} + \text{positron}
\]
Mass number \(A\) stays the same
Atomic number \(Z\) decreases by 1
6) Gamma decay
No change to \(A\) or \(Z\)
Releases energy only
Example: gamma emission often happens after alpha or beta decay.
7) Penetration and ionisation
Penetration: alpha < beta < gamma
Ionisation: gamma < beta < alpha
Memory trick: alpha is easily stopped but causes lots of ionisation.
8) Half-life
\[
N=N_0\left(\frac{1}{2}\right)^n
\]
where \(n=\frac{\text{time}}{t_{1/2}}\)
Example: 1000 atoms after 3 half-lives:
\[
1000\left(\frac12\right)^3=125
\]
9) Mass defect and energy
\[
\Delta m = \text{mass of separated nucleons} - \text{mass of nucleus}
\]
\[
E=mc^2
\]
Mass defect becomes binding energy.
10) Fission and fusion
Fission: a heavy nucleus splits into smaller nuclei, releasing energy and neutrons.
Used in nuclear reactors
Control rods absorb neutrons
Moderator slows neutrons
Fusion: light nuclei join together.
Powers the Sun and stars
Example: uranium fission in a reactor can release a chain reaction if not controlled.
Page 4 — Electricity, Circuits & Exam Traps
1) Core equations
\[
I=\frac{Q}{t},\quad V=\frac{E}{Q},\quad V=IR
\]
\[
P=VI=I^2R=\frac{V^2}{R}
\]
Example: if \(V=12\,\text{V}\) and \(R=6\,\Omega\), then \(I=2\,\text{A}\).
2) Series circuits
Current is the same everywhere
Voltages add
Resistances add
Example: two resistors \(2\Omega\) and \(3\Omega\) in series give total resistance \(5\Omega\).
3) Parallel circuits
Voltage is the same across each branch
Currents add
Use
\[
\frac{1}{Rt}=\frac{1}{R1}+\frac{1}{R_2}+...
\]
Example: parallel circuits reduce total resistance.
4) Meters
Ammeter: connected in series, very low resistance
Voltmeter: connected in parallel, very high resistance
Exam trap: an ammeter in parallel can damage the circuit.
5) LDR and thermistor
LDR: more light → lower resistance
NTC thermistor: higher temperature → lower resistance
Example: street lights can use LDRs to switch on when it gets dark.
6) RCD safety switch
Detects a current imbalance and cuts power quickly to reduce electric shock risk.
7) Common 1-mark answers
Why is frequency unchanged in refraction? It is determined by the source.
Why does evaporative cooling happen? The highest-energy particles escape, lowering average kinetic energy.
Why do optical fibres work? Total internal reflection.
Why does violet bend more? It has a shorter wavelength and higher refractive index.
Why does the greenhouse effect happen? Greenhouse gases absorb and re-radiate infrared radiation.
8) Must memorise
\(c=3.0\times10^8\,\text{m/s}\)
Wien constant \(=2.898\times10^{-3}\,\text{m K}\)
Air refractive index \(\approx 1.00\)
Alpha quality factor \(=20\)
Beta/Gamma quality factor \(=1\)
Quick exam tips
Always check units first.
Write the formula before substituting numbers.
For decay questions, track both mass number and atomic number.
For refraction, remember: frequency stays the same.
For thermal questions, decide whether the energy is changing temperature or causing a state change.
Mini practice
A wave has frequency \(8\,\text{Hz}\) and wavelength \(0.5\,\text{m}\). Find speed.
Why does light bend toward the normal when entering water from air?
What happens to \(A\) and \(Z\) in beta minus decay?
State the difference between conduction and convection.
Why does a voltmeter need very high resistance?