GCE Advanced Level (A-Levels) Physics Syllabus

How is internal resistance found from a graph of terminal p.d. $V$ against current $I$?

Rearranging $V = \varepsilon - Ir$ shows the graph is a straight line: the y-intercept gives the e.m.f. $\varepsilon$ and the gradient is $-r$ (so internal resistance is the magnitude of the gradient).

Define the wavelength, frequency and period of a wave, and state the wave equation.

Wavelength $\lambda$ is the distance between adjacent points in phase. Frequency $f$ is the number of cycles per second. Period $T = 1/f$. Wave equation: $v = f\lambda$.

Distinguish transverse and longitudinal waves, with an example of each.

Transverse: oscillations are perpendicular to the direction of energy transfer (e.g. light, water waves). Longitudinal: oscillations are parallel to the direction of energy transfer, forming compressions and rarefactions (e.g. sound).

Define phase difference and give it for two points one wavelength apart.

Phase difference is the difference in the stage of oscillation between two points, measured in radians or degrees. Points one wavelength apart have a phase difference of $2\pi$ rad ($360^{\circ}$), i.e. they are in phase.

What does it mean for light to be plane polarised, and what waves can be polarised?

Plane polarised light has oscillations restricted to a single plane. Only transverse waves can be polarised; longitudinal waves cannot.

State the principle of superposition.

When two or more waves meet at a point, the resultant displacement equals the vector sum of the individual displacements at that point.

What conditions are required for two sources to produce a stable interference pattern?

The sources must be coherent (constant phase difference, same frequency) and ideally have similar amplitude. The waves must also overlap and (for clear fringes) be of the same type and similarly polarised.

State the conditions for constructive and destructive interference in terms of path difference.

Constructive: path difference $= n\lambda$ (whole number of wavelengths). Destructive: path difference $= \left(n + \tfrac{1}{2}\right)\lambda$, where $n$ is an integer.

Describe how a stationary wave forms and define nodes and antinodes.

A stationary wave forms when two waves of the same frequency and amplitude travel in opposite directions and superpose. Nodes are points of zero amplitude (destructive); antinodes are points of maximum amplitude (constructive). Adjacent nodes are $\tfrac{\lambda}{2}$ apart.

For a stretched string fixed at both ends, give the wavelength of the first harmonic (fundamental) and its frequency formula.

First harmonic: $\lambda = 2L$. Frequency $f = \dfrac{1}{2L}\sqrt{\dfrac{T}{\mu}}$, where $T$ is tension and $\mu$ is mass per unit length.

State the double-slit (Young's) fringe spacing equation.

$w = \dfrac{\lambda D}{s}$, where $w$ is the fringe spacing, $\lambda$ the wavelength, $D$ the slit-to-screen distance, and $s$ the slit separation.

State the diffraction grating equation and identify the terms.

$d\sin\theta = n\lambda$, where $d$ is the grating spacing (distance between adjacent slits), $\theta$ the angle of the maximum, $n$ the order, and $\lambda$ the wavelength.

Describe the appearance of the single-slit diffraction pattern for monochromatic light.

A wide, bright central maximum with much dimmer maxima on either side. The central maximum is twice the width of the others, and intensity decreases for higher orders.

State Snell's law of refraction and define the refractive index of a medium.

$n_{1}\sin\theta_{1} = n_{2}\sin\theta_{2}$. The refractive index $n = \dfrac{c}{v}$, the ratio of the speed of light in vacuum to its speed in the medium ($n \geq 1$).

Define the critical angle and state its relationship to refractive index.

The critical angle $\theta_{c}$ is the angle of incidence for which the refracted ray travels along the boundary ($\theta_{2}=90^{\circ}$). For light going from a denser medium $n_{1}$ to less dense $n_{2}$: $\sin\theta_{c} = \dfrac{n_{2}}{n_{1}}$. Beyond it, total internal reflection occurs.

Distinguish material dispersion and modal dispersion in optical fibres.

Material (spectral) dispersion: different wavelengths travel at different speeds, broadening the pulse — reduced using monochromatic light. Modal dispersion: rays taking different paths arrive at different times — reduced using a thin/single-mode core. Both cause pulse broadening, limiting data rate.

State Newton's law of gravitation.

The gravitational force between two point masses is attractive and given by $F = \dfrac{Gm_{1}m_{2}}{r^{2}}$, where $G$ is the gravitational constant and $r$ the separation of the centres of mass.

Define gravitational field strength and give it for a radial field.

Gravitational field strength is the force per unit mass: $g = \dfrac{F}{m}$. For a radial field around a point/spherical mass $M$: $g = \dfrac{GM}{r^{2}}$. Units: $\text{N\,kg}^{-1}$ ($\text{m\,s}^{-2}$).

Give the expression for gravitational potential in a radial field and state its sign.

$V = -\dfrac{GM}{r}$. It is always negative because the potential is defined as zero at infinity and work must be done to move a mass away from the field. Units: $\text{J\,kg}^{-1}$.

State Coulomb's law for the force between two point charges.

$F = \dfrac{1}{4\pi\varepsilon_{0}}\dfrac{Q_{1}Q_{2}}{r^{2}}$, where $\varepsilon_{0}$ is the permittivity of free space. The force is repulsive for like charges and attractive for unlike charges.

Define electric field strength and give expressions for a radial field and a uniform field.

Electric field strength is force per unit positive charge: $E = \dfrac{F}{Q}$. Radial field: $E = \dfrac{1}{4\pi\varepsilon_{0}}\dfrac{Q}{r^{2}}$. Uniform field between parallel plates: $E = \dfrac{V}{d}$. Units: $\text{N\,C}^{-1}$ or $\text{V\,m}^{-1}$.

Define capacitance and state the energy stored on a capacitor.

Capacitance $C = \dfrac{Q}{V}$ (units: farads). Energy stored: $E = \tfrac{1}{2}QV = \tfrac{1}{2}CV^{2} = \dfrac{Q^{2}}{2C}$ (area under a charge–voltage graph).

Give the equation for capacitor discharge through a resistor and define the time constant.

$Q = Q_{0}e^{-t/RC}$ (and $V$, $I$ follow the same form). The time constant is $\tau = RC$, the time for the charge to fall to $\tfrac{1}{e}$ ($\approx 37\%$) of its initial value.

Give the magnitude of the magnetic force on a current-carrying conductor and on a moving charge.

On a wire: $F = BIL\sin\theta$. On a moving charge: $F = Bqv\sin\theta$, where $\theta$ is the angle between the velocity/current and the magnetic flux density $B$ (units: tesla). Direction given by Fleming's left-hand rule.

State Faraday's law and Lenz's law of electromagnetic induction.

Faraday's law: the induced e.m.f. is proportional to the rate of change of flux linkage, $\varepsilon = -N\dfrac{\Delta\Phi}{\Delta t}$. Lenz's law: the induced current opposes the change producing it (the source of the minus sign / conservation of energy). Flux linkage $= N\Phi = NBA$.

Distinguish particles and antiparticles, and give the electron's antiparticle.

An antiparticle has the same mass and rest energy as its particle but opposite charge (and other quantum numbers). The electron's antiparticle is the positron, with charge $+e$. A particle and its antiparticle annihilate to produce energy (photons).

State the photoelectric equation and what it tells us about light.

$hf = \phi + E_{k(\max)}$, where $hf$ is the photon energy, $\phi$ the work function, and $E_{k(\max)}$ the maximum kinetic energy of emitted electrons. It shows light is quantised into photons; emission occurs only above the threshold frequency.

Give the de Broglie wavelength equation and the photon energy equation.

De Broglie wavelength: $\lambda = \dfrac{h}{p} = \dfrac{h}{mv}$. Photon energy: $E = hf = \dfrac{hc}{\lambda}$, where $h$ is the Planck constant.

Define the half-life of a radioactive isotope and give the decay equation.

Half-life $t_{1/2}$ is the average time for half the nuclei in a sample to decay (or for activity to halve). Decay: $N = N_{0}e^{-\lambda t}$ and activity $A = \lambda N$, where $\lambda$ is the decay constant, related by $t_{1/2} = \dfrac{\ln 2}{\lambda}$.

Compare the nature, charge and penetrating power of alpha, beta-minus and gamma radiation.

Alpha ($\ce{^{4}_{2}He}$ nucleus, charge $+2e$): highly ionising, stopped by paper/few cm of air. Beta-minus (electron, charge $-e$): moderately ionising, stopped by a few mm of aluminium. Gamma (EM photon, no charge): weakly ionising, reduced by thick lead/concrete.

State Einstein's mass–energy equation and explain binding energy.

$E = mc^{2}$. Binding energy is the energy released when nucleons bind into a nucleus, equal to the mass defect times $c^{2}$. Iron-56 has the highest binding energy per nucleon, so fusion of light nuclei and fission of heavy nuclei both release energy.

State the ideal gas equation in both molar and molecular forms.

Molar form: $pV = nRT$ ($n$ = number of moles, $R$ = molar gas constant). Molecular form: $pV = NkT$ ($N$ = number of molecules, $k$ = Boltzmann constant). Temperature $T$ is in kelvin.

State the kinetic theory equation for pressure and the relation between mean kinetic energy and temperature.

$pV = \tfrac{1}{3}Nm\overline{c^{2}}$, where $\overline{c^{2}}$ is the mean square speed. Mean translational kinetic energy per molecule: $\tfrac{1}{2}m\overline{c^{2}} = \tfrac{3}{2}kT$, so it is directly proportional to absolute temperature.

Define angular velocity and give the equations for centripetal acceleration.

Angular velocity $\omega = \dfrac{\Delta\theta}{\Delta t} = \dfrac{2\pi}{T} = 2\pi f$, with $v = \omega r$. Centripetal acceleration: $a = \dfrac{v^{2}}{r} = \omega^{2}r$, directed towards the centre.

Give the equation for centripetal force and state its direction.

$F = \dfrac{mv^{2}}{r} = m\omega^{2}r$. It acts towards the centre of the circle. It is a resultant force (provided by tension, gravity, friction, etc.), not a new type of force, and does no work since it is perpendicular to motion.

Define simple harmonic motion (SHM) and state its defining equation.

SHM is oscillation where acceleration is proportional to displacement from equilibrium and directed towards it: $a = -\omega^{2}x$. The restoring force is proportional to displacement and opposite in direction.

For SHM, give the equations for displacement, maximum speed and maximum acceleration.

Displacement (starting at amplitude): $x = A\cos(\omega t)$. Speed: $v = \pm\omega\sqrt{A^{2}-x^{2}}$, with maximum speed $v_{\max} = \omega A$. Maximum acceleration $a_{\max} = \omega^{2}A$ (at the extremes).

Give the period equations for a simple pendulum and a mass–spring system.

Simple pendulum: $T = 2\pi\sqrt{\dfrac{L}{g}}$. Mass–spring: $T = 2\pi\sqrt{\dfrac{m}{k}}$. Both are independent of amplitude (isochronous for small oscillations).

Describe the energy exchange in SHM and define resonance.

In SHM, energy interchanges between kinetic and potential while total energy stays constant (no damping). Kinetic energy is maximum at equilibrium, potential maximum at the extremes. Resonance occurs when a system is driven at its natural frequency, giving maximum amplitude.

Distinguish light, critical and heavy damping.

Light damping: amplitude decreases gradually over many oscillations. Critical damping: returns to equilibrium in the shortest time without oscillating. Heavy (over) damping: returns slowly to equilibrium without oscillating.