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LearnEdexcelYPH112018 specificationWPH12 · Unit 2: Waves and ElectricityWaves and the particle nature of light

WPH12 · Module

Waves and the particle nature of light

9 subtopics≈ 330 min in total

Start the module: Photons and the photoelectric effect Open graphing calculator

Photons and the photoelectric effect
Light comes in quanta called photons, each of energy $E=hf=\dfrac{hc}\lambda$ ( $h=6.63\times10^{-34}$ J s) and momentum $p=\dfrac Ec$ . When photons hit a metal, each can release one electron if its energy exceeds the work function $\Phi$ : $hf=\Phi+\tfrac12mv_{\max}^2$ . Below the threshold frequency $f_0=\dfrac\Phi h$ , no electrons are emitted, however bright the light. Brighter light means more photons, so more electrons, but not faster ones.
≈ 40 min
Stationary waves
When two identical progressive waves travel in opposite directions, they superpose to form a stationary wave. Nodes (zero amplitude) and antinodes (maximum amplitude) stay in fixed places, $\tfrac\lambda2$ apart. No energy is carried along. On a string fixed at both ends the fundamental has $\lambda=2L$ ; in a pipe closed at one end, $\lambda=4L$ .
≈ 40 min
Progressive waves and intensity
A progressive wave transfers energy without transferring matter. Points one wavelength apart oscillate in phase; points half a wavelength apart are in antiphase. Phase difference (in degrees or radians) $=\dfrac{x}{\lambda}\times360^\circ$ . Intensity, the power per unit area, is proportional to amplitude squared, and falls with the inverse square of distance from a point source.
≈ 35 min
Wave–particle duality
Light behaves as a wave (diffraction, interference) and as particles (the photoelectric effect). Matter does too: de Broglie proposed that any moving particle has a wavelength $\lambda=\dfrac hp=\dfrac h{mv}$ . Electron diffraction through thin graphite proves it: electrons form rings like waves passing through a grating. Faster electrons have shorter wavelengths, so the rings get smaller.
≈ 35 min
Diffraction and interference
Waves spread out (diffract) through gaps about the size of their wavelength. Two coherent sources produce an interference pattern: bright fringes where the path difference is a whole number of wavelengths, dark fringes where it's a half-integer. For Young's double slits, fringe spacing $x=\dfrac{\lambda D}a$ .
≈ 40 min
The diffraction grating
A diffraction grating has thousands of equally spaced slits. Maxima appear only at angles where light from every slit arrives in phase: $d\sin\theta=n\lambda$ , with $d$ the slit spacing. The maxima are much sharper and brighter than with two slits, so gratings measure wavelengths precisely and split light into spectra.
≈ 35 min
Electromagnetic spectrum and polarisation
All electromagnetic waves are transverse and travel at $3.00\times10^8$ m s⁻¹ in free space. Wavelengths run from kilometres (radio) to less than $10^{-11}$ m (gamma); visible light is $400$ – $700$ nm. Only transverse waves can be polarised. A polariser halves unpolarised light; after that, Malus's law gives $I=I_0\cos^2\theta$ .
≈ 30 min
Energy levels and line spectra
Electrons in an isolated atom can only have certain discrete energies, called energy levels (negative values, with zero meaning the electron is free). When an electron drops from level $E_1$ to a lower level $E_2$ , it emits a photon with $hf=E_1-E_2$ . Because only certain differences exist, only certain wavelengths appear: a line spectrum. An absorption spectrum shows dark lines where the atoms absorb exactly those photon energies from a continuous spectrum.
≈ 35 min
Refraction and optical fibres
Light slows down in a material; the refractive index is $n=\frac cv$ . At a boundary, $n_1\sin\theta_1=n_2\sin\theta_2$ (Snell's law). Going into a less dense medium, beyond the critical angle $\sin C=\frac{n_2}{n_1}$ all the light reflects: total internal reflection. Optical fibres trap light this way, using a core surrounded by cladding of lower refractive index.
≈ 40 min