Only transverse waves can be polarised, and light can.
Every electromagnetic wave is transverse and travels at c in a vacuum; only the wavelength differs.

Stationary waves on strings

In an ideal stationary wave, there is no net energy transfer along the string.
Adjacent nodes are half a wavelength apart.

Stationary waves in air columns

A closed end is a node and an open end an antinode.
A closed tube fits an odd number of quarter wavelengths, so it sounds only the odd harmonics.
In the resonance tube it is the difference of two lengths that gives the wavelength.

Refraction and Snell's law

Angles are measured from the normal.
Frequency survives a boundary; speed and wavelength do not.

Total internal reflection and optical fibres

TIR needs a lower n on the far side,
and an angle past the critical one.

Diffraction and the single slit

Every gap diffracts, and a gap near λ diffracts most.

Interference and Young's double slit

Bright where the paths differ by nλ.
Dark where they differ by (n + ½)λ.

Diffraction gratings

d sin θ = nλ.
sin θ can never pass 1, and that caps n.

Lenses and images

Power is one over the focal length, in metres.
Powers of lenses in contact add.
Real is positive, so a negative v is a virtual image.

Quantum phenomenaYear 125 topics

The photoelectric effect and the photon

Frequency sets whether electrons leave, and how fast.
Brightness sets only how many.

The photoelectric graph and measuring h

The gradient is h, a universal constant; the intercepts are φ and f0 and belong to the metal.
The LED method gives an estimate of h, and the word estimate is part of the answer.

Collisions of electrons with atoms

Atoms accept exact gaps, or nothing.
A fluorescent tube chains ionisation, excitation, ultraviolet emission and phosphor re-emission.

Energy levels and photon emission

Discrete lines mean discrete gaps.
Discrete gaps mean discrete levels.
One transition makes exactly one photon.

Wave-particle duality

Photons and matter particles can produce interference and diffraction, while detections occur as localised events. Which behaviour is observed depends on the measurement arrangement.

ParticlesYear 129 topics

Constituents of the atom

Z is the proton number and identifies the element.
A is the nucleon number.
Specific charge is Q/m.

Stable and unstable nuclei

The strong force attracts out to 3 fm and repels inside 0.5 fm.
Every decay balances A and Z exactly.
The antineutrino exists because the beta spectrum is continuous.

Antimatter and photons

Same mass, opposite charge and opposite quantum numbers, every particle.
Rest energy sets the threshold in both directions.

Particle interactions and exchange particles

In the Standard Model, interactions are described as mediated by gauge bosons.
Gravity has no tested exchange particle, and the graviton stays a proposal.
Only the weak interaction changes quark flavour.

Classification of particles

Hadrons feel the strong force. Leptons are fundamental.
Strong interactions conserve strangeness, so strange particles are created in pairs; weak interactions may change it.

Quarks and the hadrons built from them

Baryons are three quarks. Mesons are a quark with an antiquark.
Antiquarks flip every sign.
Add thirds: every hadron's charge comes out whole.

Decays at quark level

Write the quark content under both sides and find the one quark that changed flavour.
The neutron's decay is one d becoming a u.
Only the weak interaction changes flavour, so a change of strangeness names the interaction.

The conserved quantities

Check conservation of charge, baryon number, lepton number and strangeness.
One failed row is enough to forbid an interaction, and it is also the reason to quote.

Energy, momentum and particle tracks

Energy and momentum must be conserved as well, and either alone can forbid an interaction.
On a photograph, no track means a neutral particle, the curl gives the sign and the radius gives the momentum.

ElectricityYear 1210 topics

Current, charge and potential difference

Current is charge per second; potential difference is joules per coulomb.
One volt is one joule per coulomb, not one joule per electron.

Charge carriers, drift speed and resistance

Conventional current is the direction of positive-charge flow, from + to −.
In a metal the electrons drift in the opposite direction.
Both statements hold at once, so label which quantity each direction describes.

Current-voltage characteristics

R is the ratio V over I at a point, never the gradient of a curve.

Resistivity and temperature

R belongs to the wire.
ρ belongs to the material.

Light-dependent resistors and superconductivity

Light frees carriers, so n rises and R falls; warming a metal scatters the carriers it already has, so R rises.
Below the critical temperature the resistivity is exactly zero, not very small.

Circuit symbols and Kirchhoff's laws

Charge is conserved at every junction.
Energy is conserved round every loop.

Series, parallel and power

Series shares the current.
Parallel shares the pd.
Adding a parallel branch provides another path for current, so the combined resistance falls below the resistance of either branch.

The potential divider and its output

One current, so the shares follow the resistances.

Sensing circuits and the potentiometer

Changing one resistance changes how the supply pd is shared.
At balance no current flows in the branch, so a potentiometer reads an emf and not a terminal pd.

EMF and internal resistance

The emf is the energy per coulomb the cell supplies.
The terminal pd is what is left after the internal resistance.
The difference, Ir, grows with the current.

Periodic motionYear 135 topics

Circular motion

Circular motion is accelerated motion, aimed at the centre.
Something real has to supply the force.

Simple harmonic motion

Acceleration is proportional to displacement and directed towards equilibrium.
The period does not depend on the amplitude.

The mass on a spring and the simple pendulum

A mass-spring period depends on m and k; a pendulum period on l and g.
Neither formula contains the amplitude, and the pendulum's does not contain the mass.

Energy in an oscillation and damping

Energy transfers between kinetic and potential; the total is constant while nothing damps it.
The energy varies at twice the frequency of the motion.
Damping reduces the amplitude, and light damping changes the period only slightly.

Forced vibrations and resonance

Resonance occurs when the driving frequency equals the system's natural frequency.
Heavier damping lowers and broadens the response peak.

Thermal physicsYear 135 topics

Internal energy and changes of state

Internal energy is random KE plus PE, summed over the particles.
Heating and working are the only two ways in.
A state change spends the energy on PE, so T stands still.

Specific heat capacity and latent heat

Q = mcΔθ while the temperature moves, Q = ml while it stands still, and a problem that crosses a state change is one Q per stage added up.
Δθ is a difference, so it is the same number in °C and in K and needs no conversion.
The electrical experiments cancel their losses with a second run rather than by lagging: same temperature, different power, and the difference is what the substance took.

Ideal gases and the gas laws

Kelvin in every gas law, no exceptions.
Use pV = nRT when the amount is given in moles and pV = NkT when it is given as a number of molecules.

The kinetic theory model and its derivation

Pressure is bombardment, derived from momentum.
c_rms is square, average, then root.

What temperature means for a gas

Mean molecular kinetic energy is proportional to absolute temperature, and equals (3/2)kT.
At one temperature a lighter molecule must move faster to carry the same energy.
An ideal gas keeps no potential energy at all.

Gravitational fieldsYear 134 topics

The field concept

A force field is a region in which a body experiences a non-contact force.
Gravitational and electric fields have analogous mathematical descriptions, but gravity is always attractive whereas electric forces may attract or repel.

Newton's law of gravitation

Every mass pulls every other with an inverse-square force.
Field strength is force per unit mass.
Measure r from the centre of the body, not from its surface.

Gravitational potential

Potential is the work per kilogram to arrive from infinity, and it is always negative.
Gradient gives g from V; area gives ΔV from g.

Orbits and satellites

Kepler: an ellipse with the Sun at one focus, equal areas in equal times, and T² ∝ r³.
Gravity is the centripetal force; T² grows as r³.
Lower orbit, faster satellite, lower total energy.
Geostationary: a circular equatorial orbit in the Earth's rotation direction, with a period of one sidereal day.

Electric fieldsYear 133 topics

Coulomb's law and electric field strength

Coulomb's law has the same inverse-square dependence as Newton's law of gravitation, with charge replacing mass.
Between parallel plates E = V/d, and a charge entering at right angles follows a parabola.

Electric potential

Potential is work per coulomb from infinity, and its sign follows the charge.
The size of the V against r gradient gives E, and the field points down the gradient; the area under E against r gives ΔV.
A volt is a joule per coulomb, never an amount of energy on its own.

Comparing electric and gravitational fields

Both forces follow inverse-square laws. Between two protons, the electric force is about 10³⁶ times stronger than gravity; on astronomical scales, electrical neutrality leaves gravity dominant.

CapacitanceYear 134 topics

Capacitors and the dielectric

Capacitance is the charge stored per unit potential difference: C = Q/V.
A dielectric between the plates increases it.
In the plate formula A sits on top, d underneath, and ε_r multiplies the rating.

Energy stored and capacitor combinations

The energy stored is the area under a graph of V against Q, ½QV, and is proportional to the pd squared.
In parallel capacitances add; in series their reciprocals do, each the reverse of the resistor rule.

Charging and discharging

On discharge, Q, V and the current magnitude decay exponentially along the same curve.
On charging, Q and V rise while the current starts at V/R and falls to zero.

The time constant and exponential decay

The time constant is RC: with R in ohms and C in farads, it comes out in seconds.
One time constant leaves 37%; every 0.69 of one halves the charge.
Log the data and the exponential plots as a straight line.

Magnetic fieldsYear 137 topics

Magnetic flux density and the force on a wire

F = BIl sin θ; the force is perpendicular to both the current direction and the magnetic field.
One tesla exerts a force of one newton on each metre of a perpendicular wire carrying one ampere.

Force on a moving charge

For motion perpendicular to a uniform magnetic field, F = BQv. Because the force is perpendicular to the velocity, it changes direction but not speed, producing circular motion.
The radius r = mv/BQ, so the curvature of a track gives the particle's momentum.

Magnetic flux and flux linkage

Flux is the field through an area, Φ = BA; flux linkage multiplies it by the number of turns; and θ in NΦ = BAN cos θ is measured to the normal.

Electromagnetic induction: Faraday and Lenz

Emf is the rate of change of flux linkage.
Lenz's law states that the induced current opposes the change in magnetic flux that produces it. This direction is required by conservation of energy.
A coil rotating uniformly in a field gives ε = BANω sin ωt.

Alternating currents

An alternating current reverses direction periodically; the rms value is 0.707 of the peak for a sinusoid only.
Quoted ac is rms, the dc equivalent for power in the same resistor.
On an oscilloscope, divisions convert to volts and seconds, and f = 1/T.

Rectification and smoothing

A diode passes current in one direction only, and a bridge of four uses both half-cycles.
A reservoir capacitor discharges through the load between peaks; the ripple falls as RC increases.

Transformers

The turns ratio sets the voltage ratio, and the output power cannot exceed the input power.
For a given transmitted power, increasing the voltage reduces the current. This reduces cable losses because P_loss = I²R.

Nuclear physicsYear 138 topics

Rutherford scattering and the nuclear model

Most alphas missed, so the atom is nearly all empty space.
The rare rebounds mark a nucleus that is tiny, massive and positive.
Every revision of the model began as a surprise in somebody's data.

Alpha, beta and gamma radiation

Alpha radiation is stopped by paper or a few centimetres of air; beta is stopped by a few millimetres of aluminium; gamma is penetrating and is reduced, rather than completely stopped, by thick lead or concrete.
Double the distance from a gamma source and a quarter of the intensity remains.
Subtract the background before any count rate does any work.

Radioactive decay and the decay constant

A larger decay constant corresponds to a shorter half-life. The decay time of a single nucleus is unpredictable, but a large sample has a statistically predictable exponential decay rate.
The exponential model approaches zero asymptotically. A real finite sample contains a discrete number of nuclei and may eventually contain no undecayed nuclei.

Half-life and nuclear instability

A genuine exponential halves in the same time everywhere along its length.
ln N against t is a straight line: the gradient is −λ, and the straightness is the evidence that the decay is exponential.
Above the band β⁻, below it β⁺ or electron capture, the heaviest shed alphas, and gamma changes neither N nor Z.

Nuclear radius and density

R = R₀A^(1/3), so nuclear volume simply counts nucleons.
On the radius law, medium and heavy nuclei share one density near 2 × 10¹⁷ kg m⁻³; the lightest stray furthest from it.
Closest approach only ever overestimates; electron diffraction measures.

Mass-energy and binding energy

A bound nucleus weighs less than its parts, and the gap is the binding energy.
Divide by A and iron-56 sits at the top of the curve, near 8.8 MeV per nucleon.

Fission and fusion

Fission of heavy nuclei and fusion of light nuclei both release energy because their products have greater binding energy per nucleon and lie closer to the peak of the binding-energy curve.
Sum the masses before and after; the missing u, times 931.5, is the MeV set free.

Nuclear reactors and safety

The moderator slows neutrons, control rods absorb excess neutrons to regulate the chain reaction, and the coolant transfers thermal energy from the core.
Reactor fuel is far too dilute to detonate; overheating is the real danger.
Four layers of safety: shut it down, cool it, shield it, contain it.

ElectronicsYear 1311 topics

The MOSFET as a switch

No channel below the threshold voltage, so the drain current is negligible; in saturation above it the drain current climbs roughly with the square of the excess.
A MOSFET gate is insulated, so it takes no steady current and a logic pin can switch amps.

Zener diodes and semiconductor sensors

A zener holds its breakdown voltage across the load while the series resistor drops whatever is left.
Photocurrent follows the light; the Hall voltage follows the flux density.

Tuned circuits and the Q factor

At resonance the two reactances cancel, and f0 depends on L and C alone.
Series resonance peaks the current, parallel resonance peaks the voltage, and both are a mass on a spring with L for the mass and C for the spring.
Q is the resonant frequency over the half-power bandwidth, so added resistance lowers Q, broadens the peak and admits more of the neighbouring frequencies.

Band-pass, band-stop and RC filters

Where the output is taken decides what the filter does.
A cut-off is where the output has fallen to 0.71 of full size, not where the signal stops.

The ideal op-amp and the comparator

An op-amp amplifies the difference between its inputs, and the ideal one has infinite gain, infinite input resistance, zero output resistance and infinite bandwidth.
With no feedback the op-amp only compares: a few hundred microvolts of difference send the output to a rail.

Negative feedback amplifiers

Negative feedback makes the closed-loop gain depend primarily on the resistor ratio. For an approximately fixed gain-bandwidth product, reducing gain increases bandwidth.
Inverting gain is minus Rf over Rin about a virtual earth; non-inverting gain is 1 + Rf over R1.

Summing and difference amplifiers

For a summing amplifier, each input contributes −(Rf/Rin)Vin to the output. The total output is the sum of these contributions, subject to the supply-rail limits.
The difference amplifier gives Rf over R1 times (V+ − V−), so interference shared by both inputs subtracts to nothing.
No output passes the supply rails; past them the amplifier saturates and clips.

Combinational logic

A logic gate's output depends only on its present inputs, so its whole behaviour fits in a truth table.
EOR answers 1 when the inputs differ, and EOR with AND is the half-adder; NAND and NOR are AND and OR with the answer flipped.

Flip-flops, counters and clocks

A D-type flip-flop copies its input to its output on each rising clock edge and holds it between edges, so it stores one bit.
Every toggling stage halves the frequency, so n stages divide by 2 to the n, and a gate that resets the chain early counts modulo n.
An astable's mark-to-space ratio is its high time over its low time; its duty cycle is its high time over the whole period.

Modulation and PCM

One modulating tone makes three frequencies, so AM occupies 2fM of spectrum while FM occupies 2(Δf + fM) and shrugs off amplitude noise.
Sample faster than twice the highest frequency, round to a level, send the code: PCM.

Radio propagation and data security

Ground wave follows the Earth's surface, sky wave is refracted back by the ionosphere, and space wave travels approximately line of sight and on out to a satellite.
Fibre loses least and is unaffected by electrical interference; anything transmitted can be intercepted, so confidentiality and integrity come from encryption and authentication rather than from the medium.

Engineering physicsYear 138 topics

Rotational motion and the angular equations

Rotational kinematics has direct analogues of s, v and a in θ, ω and α, and for constant α the four equations take the same algebraic form as SUVAT.
One body, one ω and one α: what differs from point to point is r, and v = ωr with a = αr gives each point its own speed.

Moment of inertia and rotational kinetic energy

I sums mr² over the body, so distance from the axis counts squared.
A spinning body stores ½Iω², so doubling the spin rate quadruples the stored energy.

Torque and angular acceleration

Torque is Fr, and it does for rotation what force does for a line: T = Iα.
T = Iα takes the net torque: opposing torques subtract first, and a steady ω means the net is zero.

Angular momentum and rotational power

No external torque means Iω is fixed, whatever internal rearranging happens.
A torque acting for a time delivers TΔt of angular momentum, however the torque and the time trade off.
Work in rotation is Tθ and power is Tω, the rotational analogues of Fs and Fv.

The first law and its sign convention

Q = ΔU + W, with W the work done by the gas: heat in becomes internal energy or work out.
Signs first: compression makes W negative, heat lost makes Q negative, and the sign of ΔU then says warmer or cooler.
At constant pressure the work is pΔV, the gas's pressure times the volume it sweeps.

Non-flow processes and p-V diagrams

Constant volume gives W = 0, isothermal gives ΔU = 0, adiabatic gives Q = 0.
On a p-V diagram, work is the area under the curve; pV is constant on an isotherm, pV^γ on a reversible adiabat of an ideal gas.

Heat engines and their efficiency

An engine taps the flow from hot to cold: W = Q_H − Q_C, rejecting Q_C is compulsory, and the ceiling is (T_H − T_C)/T_H in kelvin.
Four strokes and two revolutions make one cycle, and the area the indicator loop encloses is the work that cycle did.
Power audit: input from fuel, indicated in the cylinders, brake at the shaft, friction the gap; thermal times mechanical is overall.

Heat pumps and combined heat and power

Reversed, the cycle uses work to transfer heat from a colder region to a hotter one: COP is the useful heat over the work in, Q_C/W for a fridge and Q_H/W for a heat pump, and above 1 is normal.
Combined heat and power raises the sink temperature on purpose: less electricity from the same fuel, but the rejected heat leaves hot enough to be worth piping.

AstrophysicsYear 1313 topics

The astronomical refracting telescope

The objective makes a real image; the eye lens turns it into steeper parallel light.
In normal adjustment M is the objective's focal length over the eye lens's, and the tube is the two added.

Reflecting telescopes

A Cassegrain collects with a concave parabolic primary and folds the beam back through it with a convex secondary, to a focus behind the mirror.
Mirrors have no chromatic aberration, a parabola cures the spherical kind, and a mirror supported across its back can be built enormous.

Telescopes beyond the visible

Only visible light and radio reach sea level; infrared wants a high, dry summit and cold detectors, and ultraviolet and X-rays want orbit.
Observatories climb to get above water vapour and turbulence, not to get nearer the stars.

Resolving power, collecting power and the CCD

θ ≈ λ over D, in radians, and smaller is sharper.
The light gathered grows as the diameter squared: double the mirror and it collects four times the light.
A CCD registers about 80 per cent of the photons that reach it. Your eye manages about one per cent.

The apparent magnitude scale

Magnitude runs backwards: smaller number, brighter star, 2.51 per step.
Luminosity is the power a star emits; flux is what arrives, diluted by 4πd², and a known luminosity turns a measured flux into a distance.

Stellar distances and absolute magnitude

One parsec is the distance at which one astronomical unit subtends one arcsecond, and p = 1/d holds only in arcseconds and parsecs.
Absolute magnitude is the view from 10 parsecs; the distance modulus m − M gives d.

Black-body radiation and spectral classes

Wien reads the temperature off the peak of the curve.
Stefan turns temperature and area into power, and the fourth power dominates everything.
OBAFGKM files every star hot to cool.
Balmer lines peak at class A, because absorption needs atoms already sitting in n = 2.

The HR diagram and the life of Sun-like stars

The HR diagram maps brightness against temperature, hot on the left; only a magnitude scale runs backwards.
Sun-like stars end as white dwarfs, held up by electron degeneracy pressure below 1.4 solar masses.

Supernovae, neutron stars and black holes

Heavier stars die as core-collapse supernovae and leave a neutron star or a black hole.
A type Ia is a detonating white dwarf, standardised by its rate of decline.

The Doppler effect and red shift

Away means red, towards means blue, and the fractional shift is the speed over c.
A spectroscopic binary's lines swing red and blue once per orbit: the period of the swing is the orbital period, and its size is the orbital speed.

Hubble's law and the Big Bang

Hubble's law is v = Hd. Under the assumption of a constant expansion rate, 1/H gives an approximate age of the universe.
The Cosmological principle: homogeneous, isotropic, and one set of physical laws everywhere.

Quasars

A quasar is an active supermassive black hole, giving galaxy power from a solar-system volume.
Its flicker time caps its size, and its red shift estimates its distance.

Detecting exoplanets

Direct imaging fails for two reasons: the star is about a billion times brighter than the planet, and their angular separation is below the diffraction limit.
The transit dip is (rp/rs) squared and repeats once per orbit; the star's Doppler wobble shares that period, and its size scales with the planet's mass.

Turning pointsYear 1310 topics

Cathode rays and the electron gun

A discharge tube glows because ions freed by the pd strike the cathode and knock out particles that stream towards the anode.
Thermionic emission boils electrons off a hot filament, and eV = ½mv² sets the speed the anode pd delivers.

The specific charge of the electron

Balance eE against Bev and the beam's speed is E/B, no clock required; the gun's pd then gives e/m = v²/2V.
Thomson measured e/m, over a thousand times the hydrogen ion's value (about 1800 today).
Same charge, far less mass, so atoms must have smaller parts inside them.

Millikan's oil drop experiment

Hold the droplet still and QV/d = mg gives its charge. Let it fall and Stokes' law weighs it.
Every droplet carried a whole multiple of e, so free charge is quantised in units of the electronic charge.

Corpuscles, waves and Young's fringes

Corpuscles need light faster in glass. Waves need it slower. The measured speed decides between them.
Young's dark fringes are two lights cancelling, which particles cannot do.

Electromagnetic waves and the speed of light

Maxwell computed c from two electrical constants, and light turned out to be his wave.
Fizeau made the speed of light a terrestrial measurement, and light in water came out slower, as waves require.
Hertz made those waves in a laboratory and measured their speed at c.

Quanta and the photoelectric effect

Planck quantised energy at E = hf, and Einstein made the packets real as photons.
Photoelectricity fails wave theory three ways: the threshold, the instant emission, and intensity moving the number of electrons, never their maximum kinetic energy.

Matter waves and electron microscopes

De Broglie proposed that a particle of momentum p has wavelength λ = h/p, which electron diffraction confirmed.
λ = h/√(2meV): raise the pd and the rings tighten, and about 150 V is already enough for an atomic-scale wavelength.

The Michelson-Morley experiment

No fringe shift of the predicted size was observed, at any orientation or time of year, within the instrument's sensitivity: absolute motion is undetectable and c is invariant for every observer.

Time dilation and muon decay

A moving clock runs slow by the factor √(1 − v²/c²), and cosmic-ray muons reaching the ground are the standard evidence.
Proper time belongs to the frame where both events happen at the same place.

Length contraction, mass and energy

Moving lengths shrink along the motion by the same root that slows moving clocks, and proper length is measured at rest with the object.
Rest mass m₀ is invariant; the total energy follows E² = p²c² + (m₀c²)², and c is a limiting speed no amount of energy can reach.

Medical physicsYear 1311 topics

Ultrasound imaging

Depth is ct over two, because the echo travelled there and back.
Impedance mismatch sets how much reflects, and the gel exists to remove the worst mismatch of all.
A-scan gives one line of depths. B-scan sweeps that line into a picture.

MR scanning and the endoscope

An endoscope is total internal reflection put to work, and the bundle carrying the image must be coherent, every fibre in the same place at both ends.
MR times how quickly tipped protons relax, and the relaxation time depends on the tissue: soft-tissue detail with no ionising dose.

The physics of diagnostic X-rays

The tube pd caps the photon energy, so E max equals eV, and everything else in the beam is softer.
The smooth part of the spectrum is bremsstrahlung and stops at λ min = hc/eV; the sharp lines are characteristic of the target's own energy levels.
Attenuation is exponential, and contrast is a difference in μ between neighbouring tissues.

X-ray detectors and CT scanning

An intensifying screen lowers the dose at the expense of a little sharpness, and a flat panel reads the beam out as numbers.
A single projection superposes everything along the ray; CT reconstructs the slice from projections recorded at many angles, which is what removes the superposition.

Radionuclide imaging and the gamma camera

A tracer maps function, not shape, and the half-life that matters is the effective one: 1/T_E = 1/T_P + 1/T_B.
Photons have to be what leaves the patient, so a gamma camera takes a gamma emitter.
The camera reads in beam order: the collimator selects photon direction, the scintillator converts each photon to light, and the photomultipliers produce the signals that locate it.

PET scanning and radiotherapy

Annihilation gives two 511 keV photons back to back, and coincidence detection turns each pair into a line. The lines cross where the tracer is.
PET maps function and CT maps structure, which is why the scanner is built as both and the two images are overlaid.
A beta-minus emitter cannot reach a gamma camera because its range is millimetres, and an implant treats for exactly that reason.

The eye as an optical system

The image distance in the eye is fixed, so focusing changes the power, not the position of the lens.
The extra power the eye must supply for a near object is always 1/u, because the 1/v term never moves.
Cones give colour and detail in bright light; rods give sensitivity in the dark and lose the detail by sharing nerve fibres.

Defects of vision and their correction

Myopia is a finite far point corrected by a diverging lens; hypermetropia is too little power for the eye's length, corrected by a converging lens. A distant near point with the far point still at infinity is lost accommodation, not long sight.
Power in dioptres needs the focal length in metres, and a diverging lens has a negative power.
The correcting lens forms a virtual image where the eye can already focus, so its v always carries a minus sign.
A prescription is SPH, CYL and AXIS, and the axis names the meridian where the cylinder adds no power.

The ear and the transmission of sound

Sound crosses the ear in order: pinna, canal, eardrum, ossicles, oval window, cochlea, hair cells, nerve, passing from air to bone to fluid.
The middle ear raises the pressure by a lever and an area ratio, so the sound can get into the fluid of the cochlea.
Position along the cochlea codes pitch: each frequency disturbs its own stretch of the basilar membrane most.

Intensity, loudness and the decibel scale

Intensity is power per unit area; intensity level is ten log of it against 1.0 × 10⁻¹² W m⁻².
The scale is logarithmic because the ear judges by ratio, so +10 dB is always ten times the intensity.
Equal loudness curves dip near 3 kHz, flatten as they rise, and lift at the treble end when hearing is damaged.

Biological measurement

The ECG plots a potential difference at the skin, produced by the wave of depolarisation crossing the heart.
The amplifier needs high gain, high input impedance and low noise, and the electrodes need gel.
P is the atria depolarising, QRS the ventricles depolarising, T the ventricles repolarising.
QRS is the biggest because the ventricles carry the most muscle, and the R to R interval gives the rate.

Each topic heading links to its full lesson. See also command words and the revision checklist.