Edexcel IAL Physics: Waves and the Particle Nature of Light — Revision Notes

Condensed for the final weeks. For the full explanation, use the Waves and the Particle Nature of Light study guide.

Wave basics

v = f lambda        T = 1/f

Transverse — oscillations perpendicular to travel (light, water). Longitudinal — oscillations parallel (sound).

Only transverse waves can be polarised, because only they have oscillations in more than one plane perpendicular to travel. Polarisation is therefore the standard evidence that light is transverse — and it is why sound cannot be polarised.

Refraction and total internal reflection

n = c / v            n1 sin(theta1) = n2 sin(theta2)
critical angle:      sin(C) = n2 / n1

Total internal reflection requires two conditions: the light must be travelling from a denser to a less dense medium, and the angle of incidence must exceed the critical angle. Both are needed; giving one is a half-answer.

This is the basis of optical fibres, where the cladding has a lower refractive index than the core.

Superposition

Coherence — constant phase difference and the same frequency. Required for a stable interference pattern.

constructive:  path difference = n lambda
destructive:   path difference = (n + 1/2) lambda

grating:       d sin(theta) = n lambda

Background — beyond the specification, not examinable (Unit 2 supplies only the diffraction-grating relation above, not the double-slit fringe relation): for two-source (double-slit) interference, λ = ax/D, where fringe spacing x increases with larger slit-to-screen distance D or wavelength λ, and decreases with larger slit separation a.

Stationary waves form from two waves of equal frequency and amplitude travelling in opposite directions. Node separation is λ/2, not λ.

Standing waves and diffraction: the practicals

The speed of a transverse wave on a stretched string is:

v = sqrt(T / mu)

where T is the tension and µ is the mass per unit length — investigated directly in CORE PRACTICAL 5. CORE PRACTICAL 4 determines the speed of sound in air using a two-beam oscilloscope, signal generator, speaker and microphone.

Diffraction — the spreading of a wave through a slit or around an obstacle — is explained using Huygens’ construction, treating every point on a wavefront as a source of secondary wavelets. CORE PRACTICAL 6 uses a diffraction grating to determine the wavelength of a laser (or other) light source, applying nλ = dsinθ.

Worked example. Light of wavelength 589 nm is incident on a diffraction grating with 500 lines per mm. Find the first-order angle.

d = 1 / (500 x 1000) = 2.0 x 10^-6 m
sin(theta) = n*lambda / d = (1 x 589e-9) / 2.0e-6 = 0.2945
theta = 17.1 degrees

Intensity is power per unit area, I = P/A. A pulse-echo technique (ultrasound, radar) locates an object from the time delay of a reflected pulse; resolution is limited by the wavelength used, or the pulse duration — shorter pulses and shorter wavelengths resolve finer detail.

The photoelectric effect

E = hf = hc / lambda
hf = phi + KE_max

Work function φ — the minimum energy to remove an electron from the metal surface. Threshold frequency f₀ — below it, no emission at any intensity.

The one-photon-one-electron interaction is the entire argument. Because a single photon transfers all its energy to a single electron, and energy is not accumulated, light below the threshold frequency produces no emission however intense or however long it shines. That single fact explains all four observations:

1. No emission below f₀ regardless of intensity.
2. Emission is instantaneous above f₀.
3. KE_max depends on frequency, not intensity.
4. Intensity affects only the rate of emission.

Wave theory predicts the opposite in every case, which is why the photoelectric effect is the evidence that light is particulate.

Wave–particle duality

de Broglie:  lambda = h / p = h / mv

Electron diffraction is the evidence: electrons produce diffraction rings through a thin graphite film, and diffraction is a wave property. Together with the photoelectric effect, this establishes that both light and matter show wave and particle behaviour depending on the experiment.

Energy levels

Electron energy levels are discrete and negative (zero is defined at infinite separation).

hf = E2 - E1

Line spectra are discrete because energy levels are discrete — only photons of exactly the right energy can be emitted or absorbed. Emission lines come from electrons falling; absorption lines from photons being absorbed. Each element’s pattern is unique, which is how stellar composition is determined.

Exam traps

• Saying sound can be polarised.
• Giving only one condition for total internal reflection.
• Using λ instead of λ/2 for node separation.
• Saying intense red light will eventually eject electrons.
• Omitting the minus sign on energy levels.

Self-test

1. Why can only transverse waves be polarised, and what does that prove about light?
2. Give both conditions for total internal reflection.
3. Why does intensity not overcome the threshold frequency?
4. What is the evidence for the wave nature of electrons?
5. Why are line spectra discrete?

Answers: 1. Only transverse waves oscillate in planes perpendicular to the direction of travel, so their oscillations can be restricted to one plane; the fact that light can be polarised shows it is transverse. 2. Light must pass from a denser to a less dense medium, and the angle of incidence must exceed the critical angle. 3. One photon interacts with one electron and transfers all its energy at once; increasing intensity supplies more photons but each still carries too little energy, and energy is not accumulated. 4. Electron diffraction — electrons passing through a thin graphite film produce diffraction rings, which is a wave phenomenon. 5. Electron energy levels are discrete, so only photons whose energy exactly matches a difference between two levels can be emitted or absorbed.