This mini-lesson covers the core of Eduqas Component 3 — Sections 1–10: the nature of waves, wave properties, refraction of light, photons, lasers, nuclear decay, particles and nuclear structure, nuclear energy, magnetic fields and electromagnetic induction.
⚠️ About the options — read this. Component 3 has a Section B containing four options: A Alternating Currents, B Medical Physics, C The Physics of Sports and D Energy and the Environment. You study exactly ONE of them — the one your school has chosen — and answer questions on that one only. This mini-lesson covers the core (Sections 1–10) that everybody must know. There is a separate mini-lesson for each option.
Where it sits: Component 3 is a 2 h 15 min paper worth 37.5% of the A level, and includes synoptic questions. Press Start when you are ready.
1–2. Waves and wave properties
Progressive waves, superposition and stationary waves
A progressive wave transfers energy without transferring matter. In a transverse wave the oscillations are perpendicular to the direction of travel; in a longitudinal wave they are parallel to it. Only transverse waves can be polarised.
c = fλPoints on a wavefront all oscillate in phase; rays (the propagation directions) are at right angles to the wavefronts.
Superposition: where waves meet, displacements add. Coherent sources are monochromatic with a constant phase relationship and oscillations in the same direction — without coherence, the interference pattern washes out.
λ = ay / D (Young's double slit)a = slit separation, y = fringe spacing, D = slit-to-screen distance. Constructive interference where the path difference is nλ; destructive where it is (n + ½)λ.
d sin θ = nλ (diffraction grating)Because d is very small, the orders are spread far more widely than double-slit fringes, and because there are thousands of slits, the maxima are far sharper. That is why gratings, not double slits, are used for precision spectroscopy.
Stationary waves are the superposition of two progressive waves of equal amplitude and frequency travelling in opposite directions. They store energy rather than transferring it; adjacent nodes are λ/2 apart, and every point between two nodes oscillates in phase.
Specified practicals: wavelength using Young's double slits; wavelength using a diffraction grating; the speed of sound using stationary waves; intensity variations for polarisation.
Calculate
Your turn — diffraction grating
1Light of wavelength 589 nm is shone normally onto a grating with 500 lines per mm. Calculate the angle of the second-order maximum.
°
Hint: d = 1 mm ÷ 500 = 2.0 × 10⁻⁶ m. sin θ = nλ/d = (2 × 589 × 10⁻⁹) ÷ 2.0 × 10⁻⁶ = 0.589. θ = sin⁻¹(0.589).
Quick check
Nodes and wavelength
?On a stationary wave, the distance between adjacent nodes is measured as 0.30 m. What is the wavelength?
3. Refraction of light
Snell's law, TIR and optical fibres
n = c / v · n₁ sin θ₁ = n₂ sin θ₂Snell's law. It follows directly from the wave model: the part of the wavefront entering the slower medium first is held back, so the wavefront pivots.
sin θC = n₂ / n₁Total internal reflection needs (a) light travelling from the denser to the less dense medium, and (b) an angle of incidence greater than the critical angle.
Multimode fibre: a wide core, so rays can take many different paths. Rays that bounce steeply travel further than axial rays, so a sharp pulse of light arrives smeared out — multimode dispersion. Adjacent pulses eventually overlap, which limits both the data rate and the transmission distance.
Monomode fibre: the core is made so narrow (a few µm) that effectively only one path exists. Dispersion is almost eliminated, allowing far higher data rates over far greater distances — the backbone of the internet.
Specified practical: measurement of the refractive index of a material.
Quick check
Why monomode?
?Why does a monomode optical fibre allow a much higher data rate than a multimode fibre?
4. Photons · 5. Lasers
The photoelectric effect, spectra and lasers
E = hf = hc / λh = 6.63 × 10⁻³⁴ J s. Useful: E (eV) = 1240 ÷ λ (nm); 1 eV = 1.60 × 10⁻¹⁹ J. Visible light runs from ~700 nm (red) to ~400 nm (violet).
Ek max = hf − φEinstein's photoelectric equation. φ is the work function. A graph of Ek max against f is a straight line of gradient h and intercept −φ, cutting the f axis at the threshold frequency.
Energy levels and spectra: a photon is emitted when an electron drops between two discrete levels, with hf = E₂ − E₁ — giving a line emission spectrum. Absorb the same photon energies from a continuous spectrum and you get a line absorption spectrum. The ionisation energy is the energy needed to lift an electron from the ground state to the n = ∞ level (E = 0).
λ = h / pde Broglie. Confirmed by electron diffraction — a beam of electrons through graphite gives diffraction rings, a wave phenomenon from particles.
Lasers: in stimulated emission, an incoming photon triggers an excited atom to emit a second, identical photon — same frequency, phase and direction, which is why laser light is coherent. Amplification needs a population inversion (N₂ > N₁), which is impossible to sustain in a simple 2-level system; 3-level and 4-level schemes with pumping and a metastable state achieve it. The medium sits between two mirrors, one of which is partially transmitting. Semiconductor lasers are small, cheap and efficient — used in CD/DVD drives and telecommunications.
Specified practical: determination of h using LEDs.
Calculate
Your turn — photoelectric effect
2A metal has a work function of 2.10 eV. Light of wavelength 450 nm is shone on it. Calculate the maximum kinetic energy of the emitted electrons, in eV.
eV
Hint: Photon energy in eV = 1240 ÷ 450 = 2.76 eV. E(k max) = 2.76 − 2.10.
Quick check
What a laser needs
?What is the essential condition for a laser medium to amplify light?
Sort it
Which interaction?
Tap a property, then tap the interaction it belongs to.
💪 Strong
🌀 Weak
⚡ Electromagnetic
6. Nuclear decay
Activity, decay constant and half-life
Radioactive decay is spontaneous and random: you cannot say which nucleus will decay next or when. But with vast numbers of nuclei, the statistics are exquisitely reliable.
A = λN · N = N₀e−λt · A = A₀e−λtλ = the decay constant (probability of decay per second). Activity A is in becquerels (Bq) — one decay per second.
T½ = ln 2 / λDerived by setting N = N₀/2 in the exponential law. Equivalently A = A₀ / 2ˣ, where x = the number of half-lives elapsed (and x need not be a whole number).
Nuclear equations use the AZX notation. Alpha: A falls by 4, Z by 2. Beta-minus: A unchanged, Z rises by 1. Gamma: neither changes (the nucleus simply de-excites).
Always subtract the background count rate from every reading before analysing. Specified practicals: the dice analogy for random decay; the variation of gamma intensity with distance (an inverse square law).
Calculate
Your turn — radiocarbon dating
3Carbon-14 has a half-life of 5730 years. A wooden artefact has a C-14 activity that is 20% of that of living wood. Calculate its age, to the nearest 100 years.
Rutherford's alpha scattering showed that the atom is mostly empty space with a tiny, dense, positively charged nucleus — most alphas passed straight through, but a few came almost straight back. The plum-pudding model could not produce a Coulomb repulsion anywhere near large enough to do that.
First generation particles (the only ones examined):
Leptons: electron (e⁻, charge −1) and electron neutrino (νe, charge 0).
Quarks: up (u, +⅔e) and down (d, −⅓e).
Every particle has an antiparticle — identical except for opposite charge. A particle and its antiparticle annihilate.
Quarks are never seen in isolation: they are bound into hadrons — baryons (3 quarks: proton = uud, neutron = udd), antibaryons (3 antiquarks) and mesons (a quark–antiquark pair, e.g. pions).
Conserve: charge · lepton number · baryon numberCheck every reaction against all three. Only the weak interaction can change quark flavour, and only the weak interaction involves neutrinos.
The four interactions:gravitational (all matter, infinite range, negligibly weak except for astronomical masses) · weak (all quarks and leptons, very short range) · electromagnetic (all charged particles, infinite range) · strong (all quarks, therefore all hadrons, short range).
Quick check
Beta decay in the quark model
?In beta-minus decay a neutron (udd) becomes a proton (uud). What has happened at quark level, and which interaction is responsible?
8. Nuclear energy
Mass–energy, binding energy, fission and fusion
E = mc²The mass defect is the difference between the mass of a nucleus and the sum of its separate nucleons. Its energy equivalent is the binding energy. 1 u = 931.5 MeV.
Binding energy per nucleon measures stability. The curve rises steeply for light nuclei, peaks near iron-56 (~8.8 MeV per nucleon) and then falls slowly. Energy is released whenever the products end up higher on the curve:
Fusion of light nuclei — moving up the steep left-hand side. Releases far more energy per nucleon than fission.
Fission of a heavy nucleus — the fragments sit higher than uranium does.
Method for binding energy calculations: (1) add the masses of Z protons and (A − Z) neutrons; (2) subtract the actual nuclear mass to get Δm in u; (3) multiply by 931.5 to get the binding energy in MeV; (4) divide by A for the binding energy per nucleon.
Calculate
Your turn — binding energy per nucleon
4The helium-4 nucleus has a mass of 4.00151 u. A proton is 1.00728 u and a neutron is 1.00867 u. Calculate the binding energy per nucleon, in MeV. (1 u = 931.5 MeV)
MeV
Hint: Separate nucleons: 2(1.00728) + 2(1.00867) = 4.03190 u. Δm = 4.03190 − 4.00151 = 0.03039 u. Binding energy = 0.03039 × 931.5 = 28.3 MeV. Divide by 4 nucleons.
9. Magnetic fields · 10. Induction
Magnetic forces, flux and induction
F = BIl sin θ · F = Bqv sin θUse Fleming's left-hand rule for the direction of the force (thuMb = Motion, First = Field, seCond = Current). θ is the angle between the field and the current (or velocity).
Because F = Bqv is always perpendicular to v, a charged particle in a uniform magnetic field moves in a circle — the basis of the cyclotron and the synchrotron. In a uniform electric field, F = qE is constant in direction, so the particle follows a parabola (like a projectile).
B = µ₀I / 2πa (long straight wire) · B = µ₀nI (long solenoid)Adding an iron core greatly increases the field in a solenoid. Two parallel currents exert forces on each other: the same direction → attract; opposite → repel.
Hall voltage: in a current-carrying slab in a magnetic field, the charge carriers are deflected sideways until the electric field they build up balances the magnetic force. The resulting Hall voltage VH ∝ B at constant I — so a Hall probe measures flux density.
Φ = BA cos θ · flux linkage = NΦFaraday: the induced e.m.f. equals the rate of change of flux linkage. Lenz: the induced e.m.f. (and current) opposes the change producing it — which is conservation of energy in disguise.
Specified practicals: the force on a current in a magnetic field; magnetic flux density with a Hall probe.
Calculate
Your turn — force on a conductor
5A wire of length 0.15 m carrying 5.0 A lies at 30° to a magnetic field of flux density 0.40 T. Calculate the force on it.
N
Hint: F = BIl sin θ = 0.40 × 5.0 × 0.15 × sin 30° = 0.30 × 0.5.
Calculate
Your turn — Faraday's law
6A coil of 150 turns and area 2.5 × 10⁻³ m² is perpendicular to a magnetic field. The flux density falls uniformly from 0.40 T to zero in 0.050 s. Calculate the magnitude of the induced e.m.f.