Coaching Centre
The Nature of Light: review
Module 7 review: a summary of the electromagnetic spectrum, wave model, quantum model and special relativity, all the formulas in one place, how the ideas connect, key words, and a mixed HSC-style test.
Module 7 asks one question four ways: what is light? Maxwell said it is an electromagnetic wave. Young, Fresnel and Malus showed it diffracts, interferes and polarises like a transverse wave. Planck and Einstein showed it exchanges energy in quanta. Michelson, Morley and Einstein showed its speed is the same for everyone, which changed space and time themselves. Use this page to pull the pieces together before the test.
The module at a glance
| Topic | Big ideas | Key evidence |
|---|---|---|
| Electromagnetic spectrum (7A–7D) | Accelerating charges make EM waves; $c = 1/\sqrt{\mu_0\varepsilon_0}$; spectra are fingerprints of elements; stellar spectra give temperature, composition, velocity, rotation and density | Hertz's radio waves; Fizeau and Foucault's measurements of $c$; Kirchhoff's three spectra; Doppler-shifted stellar lines |
| Wave model (7E–7G) | Huygens' wavelets; diffraction; interference $d\sin\theta = m\lambda$; light is transverse; Malus's law | Young's fringes; the Poisson–Arago spot; light slower in water (Foucault); polarisation |
| Quantum model (7H–7I) | Energy is quantised, $E = hf$; light is made of photons; $K_{max} = hf - \phi$; $p = h/\lambda$ | Black-body curves and the ultraviolet catastrophe; threshold frequency and stopping voltage; Millikan's graphs |
| Special relativity (7J–7L) | Two postulates; relativity of simultaneity; time dilation; length contraction; relativistic momentum; $E = mc^2$ | Michelson–Morley; CERN pion gamma rays; muons; Hafele–Keating; GPS; Bertozzi; accelerators; annihilation and nuclear reactions |
Formulas
| Formula | Use |
|---|---|
| $c = f\lambda$ | any EM wave in a vacuum |
| $\lambda_{max} = \dfrac{b}{T}$ | peak of black-body radiation; $b = 2.898 \times 10^{-3}$ m K, $T$ in kelvin |
| $\dfrac{\Delta\lambda}{\lambda} = \dfrac{v}{c}$ | Doppler shift of star lines ($v \ll c$) |
| $d\sin\theta = m\lambda$ | bright fringes, double slit and grating |
| $\Delta y = \dfrac{\lambda L}{d}$ | double-slit fringe spacing (small angles) |
| $I = I_{max}\cos^2\theta$ | polarised light through an analyser (unpolarised light through one filter: $\tfrac{1}{2}I_0$) |
| $E = hf = \dfrac{hc}{\lambda}$ | energy of a quantum or photon |
| $K_{max} = hf - \phi$ | photoelectric effect; $eV_0 = K_{max}$, $f_0 = \phi/h$ |
| $p = \dfrac{h}{\lambda}$ | momentum of a photon |
| $t = \dfrac{t_0}{\sqrt{1 - v^2/c^2}}$ | time dilation; $t_0$ is proper time |
| $l = l_0\sqrt{1 - v^2/c^2}$ | length contraction; $l_0$ is proper length |
| $p_v = \dfrac{m_0v}{\sqrt{1 - v^2/c^2}}$ | relativistic momentum |
| $E = mc^2$ | mass–energy equivalence |
Putting it together
- Wave or particle? Light travels and spreads like a wave (diffraction, interference, polarisation) but transfers energy and momentum in whole photons (black-body radiation, photoelectric effect). Questions often ask you to choose the model that explains a given observation and justify it.
- Same constant, different roles. $c$ appears as Maxwell's prediction (7A), in $c = f\lambda$ and $E = hc/\lambda$, as the invariant speed in the postulates (7J), and as the conversion factor in $E = mc^2$ (7L).
- The spectrum links everything. Wien's law comes from black-body radiation (quantum), Doppler shifts from waves, and line spectra from quantised atomic energy levels. One stellar spectrum uses the whole module.
- Thought experiments then tests. Einstein's light beam, light clock and train are thought experiments. Every one led to predictions later confirmed by measurements (muons, atomic clocks, accelerators).
- Evaluate evidence. Many HSC questions say "evaluate" or "analyse the evidence". Describe the experiment, state what was expected under each model, give the result, and say which model it supports and how strongly.
A star's spectrum peaks at 414 nm. Its hydrogen-alpha line (lab wavelength 656.3 nm) is observed at 656.7 nm. (a) Find the star's temperature. (b) Find its radial velocity. (c) Find the energy of a photon at the peak wavelength.
Key words
| Term | Meaning |
|---|---|
| Black body | an ideal absorber and emitter whose radiation depends only on its temperature |
| Coherent | sources with the same frequency and a constant phase difference |
| Diffraction | spreading of waves through a gap or around an edge |
| Inertial frame | a frame of reference that is not accelerating |
| Proper time | time between two events measured by a clock present at both |
| Proper length | length measured by an observer at rest relative to the object |
| Rest mass | mass measured by an observer at rest relative to the object |
| Stopping voltage | the reverse voltage that just reduces the photocurrent to zero |
| Threshold frequency | the minimum frequency that causes photoemission from a given metal |
| Work function | the minimum energy needed to remove an electron from a metal surface |
| Ultraviolet catastrophe | the classical prediction of unlimited black-body intensity at short wavelengths |
Test yourself
Maxwell's calculation of the speed of electromagnetic waves used
$c = 1/\sqrt{\mu_0\varepsilon_0}$, from electrical and magnetic constants measured in the lab.
Which observation supports the particle model of light rather than the wave model?
Only quanta of energy $hf$ explain a frequency threshold that intensity can't overcome.
Light of wavelength 600 nm falls on a grating with 500 lines per mm. The angle of the first-order maximum is
$d = 2.0 \times 10^{-6}$ m; $\sin\theta = 0.30$; $\theta = 17.5°$.
Unpolarised light of intensity 40 W m⁻² passes through two filters at 45° to each other. The final intensity is
$\tfrac{1}{2} \times 40 \times \cos^2 45° = 10$ W m⁻².
A metal has a work function of $3.2 \times 10^{-19}$ J. Its threshold frequency is
$f_0 = \phi/h = 3.2 \times 10^{-19}/6.626 \times 10^{-34} = 4.8 \times 10^{14}$ Hz.
A space probe passes Earth at 0.50$c$. Its 60 s experiment is timed by its own clock. Earth observers measure the experiment as lasting
$t = 60/\sqrt{1 - 0.25} = 60/0.866 = 69$ s.
In the core of the Sun, mass is converted to energy mainly by
The proton–proton chain fuses hydrogen to helium, releasing 0.7% of the mass.
Label the photoelectric graph
Which part of the module explains each observation?
Put these discoveries in time order.
Light is a electromagnetic wave. Hotter black bodies peak at wavelengths. Photons with frequency below the frequency cannot eject electrons. A moving clock is measured to run . The equivalence of mass and is expressed by E = mc².
"Light is both a wave and a particle." Evaluate this statement with reference to experimental evidence from this module.
Wave evidence. Young's double-slit experiment produced bright and dark fringes. Dark fringes occur where the path difference is $(m + \tfrac{1}{2})\lambda$ and the waves cancel, which particles cannot do. Light diffracts through narrow gaps, spreading as predicted by Huygens' principle, and Arago's observation of a bright spot in the centre of a disc's shadow confirmed Fresnel's wave theory. Polarisation, with transmitted intensity following $I = I_{max}\cos^2\theta$, shows that light is a transverse wave. Foucault found light travels slower in water, as the wave model predicts.
Particle evidence. Black-body spectra could only be explained when Planck assumed energy is exchanged in quanta $E = hf$; classical waves predicted the ultraviolet catastrophe. In the photoelectric effect, no electrons are emitted below a threshold frequency regardless of intensity, emission is instantaneous, and $K_{max}$ depends on frequency not intensity. Einstein explained this with photons of energy $hf$, each giving its energy to one electron, $K_{max} = hf - \phi$, which Millikan confirmed. Photons also carry momentum $p = h/\lambda$, as shown by Compton scattering.
Judgement. Each model explains one set of observations and fails for the other. The statement is therefore valid in the sense of wave–particle duality: light propagates as a wave, producing interference and diffraction, but exchanges energy and momentum in discrete photons. Which behaviour is observed depends on the experiment, so a complete description of light needs both models.