Unit 2: Waves and Particle Nature of Light

This guide covers sub-topic 2.3 Waves and Particle Nature of Light, the first half of Unit 2: Waves and Electricity, from the Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics (YPH11), Issue 3 specification (first assessment June 2019). Unit 2 is a compulsory, externally assessed unit examined by a 1 hour 30 minute paper worth 80 marks, and this topic is commonly studied through applications such as medical physics or music.

Before studying this

This topic follows Unit 1 and assumes comfort with algebraic rearrangement, using sin, and plotting straight-line graphs from experimental data (y = mx + c).

Syllabus coverage

PEARSON EDEXCEL INTERNATIONAL A LEVEL PHYSICS (YPH11) — Sub-topic 2.3

Candidates will be assessed on their ability to: understand the terms amplitude, frequency, period, speed and wavelength; use the wave equation v = fλ; describe longitudinal waves in terms of pressure variation and the displacement of molecules; describe transverse waves; draw and interpret graphs representing transverse and longitudinal waves, including standing/stationary waves; CORE PRACTICAL 4: determine the speed of sound in air using a 2-beam oscilloscope, signal generator, speaker and microphone; know and understand wavefront, coherence, path difference, superposition, interference and phase; use the relationship between phase difference and path difference; know what is meant by a standing/ stationary wave, understand how such a wave is formed, and know how to identify nodes and antinodes; use the equation for the speed of a transverse wave on a string, v = √(T/µ); CORE PRACTICAL 5: investigate the effects of length, tension and mass per unit length on the frequency of a vibrating string or wire; use the equation for the intensity of radiation, I = P/A; know and understand that at the interface between medium 1 and medium 2, n₁sinθ₁ = n₂sinθ₂, where refractive index n = c/v; calculate critical angle using sinC = 1/n; predict whether total internal reflection will occur at an interface; understand how to measure the refractive index of a solid material; understand what is meant by plane polarisation; understand what is meant by diffraction and use Huygens’ construction to explain what happens to a wave when it meets a slit or an obstacle; use nλ = dsinθ for a diffraction grating; CORE PRACTICAL 6: determine the wavelength of light from a laser or other light source using a diffraction grating; understand how diffraction experiments provide evidence for the wave nature of electrons; use the de Broglie equation, λ = h/p; understand that waves can be transmitted and reflected at an interface between media; understand how a pulse-echo technique can provide information about the position of an object, and how the amount of information obtained may be limited by the wavelength of the radiation or the duration of pulses; understand how the behaviour of electromagnetic radiation can be described in terms of a wave model and a photon model, and how these models developed over time; use E = hf, relating photon energy to wave frequency; understand that the absorption of a photon can result in the emission of a photoelectron; understand the terms threshold frequency and work function and use hf = φ + ½mv²max; use the electronvolt (eV) to express small energies; understand how the photoelectric effect provides evidence for the particle nature of electromagnetic radiation; and understand atomic line spectra in terms of transitions between discrete energy levels, and how to calculate the frequency of radiation that could be emitted or absorbed in a transition between energy levels.

Wave basics and standing waves

Amplitude, frequency, period, speed and wavelength describe a wave, related by the wave equation v = fλ. A longitudinal wave (e.g. sound) has particle displacement parallel to the direction of travel, described by pressure variation; a transverse wave (e.g. light, waves on a string) has particle displacement perpendicular to the direction of travel. CORE PRACTICAL 4 determines the speed of sound in air using a 2-beam oscilloscope, signal generator, speaker and microphone.

Coherence means waves have a constant phase relationship; superposition is the addition of displacements when waves overlap, producing interference (constructive or destructive depending on path difference and phase difference). A standing (stationary) wave forms when two waves of the same frequency travelling in opposite directions superpose, producing fixed nodes (no displacement) and antinodes (maximum displacement). The speed of a transverse wave on a string is v = √(T/µ), where T is tension and µ is mass per unit length — investigated in CORE PRACTICAL 5. The intensity of radiation is I = P/A, power per unit area.

Refraction, polarisation and diffraction

At an interface between two media, Snell’s law applies: n₁sinθ₁ = n₂sinθ₂, where refractive index n = c/v (the ratio of the speed of light in a vacuum to its speed in the medium). The critical angle C, beyond which total internal reflection occurs, satisfies sinC = 1/n. Plane polarisation restricts a transverse wave’s oscillations to a single plane. Diffraction is the spreading of a wave as it passes through a slit or around an obstacle, explained using Huygens’ construction, where every point on a wavefront is treated as a source of secondary wavelets. A diffraction grating produces bright fringes where nλ = dsinθ, used in CORE PRACTICAL 6 to determine the wavelength of light from a laser or other source.

Wave-particle duality

Diffraction of electrons provides evidence for the wave nature of particles, described by the de Broglie equation, λ = h/p, relating a particle’s wavelength to its momentum. Waves can be transmitted and reflected at an interface, and a pulse-echo technique (e.g. ultrasound or radar) can locate an object, with resolution limited by the wavelength of the radiation or the duration of the pulses used.

Electromagnetic radiation can be described by both a wave model and a photon model, whose relative usefulness has developed historically. E = hf relates photon energy to wave frequency. In the photoelectric effect, absorbing a photon can eject a photoelectron from a metal surface only if the photon’s frequency exceeds the threshold frequency; the work function φ is the minimum energy needed to release an electron, related by:

hf = φ + ½mv²max

Small energies in this context are conveniently expressed in electronvolts (eV). The photoelectric effect — instantaneous emission above a threshold frequency, independent of intensity — provides direct evidence for the particle (photon) nature of electromagnetic radiation, which a purely wave model cannot explain. Atomic line spectra arise from electron transitions between discrete energy levels, with the frequency of emitted or absorbed radiation calculated from the energy difference between levels using E = hf.

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

Grating spacing: d = 1 / (500 × 1000) m = 2.0 × 10⁻⁶ m.

Using nλ = dsinθ with n = 1:

sinθ = nλ/d = (1 × 589 × 10⁻⁹) / (2.0 × 10⁻⁶) = 0.2945

θ = sin⁻¹(0.2945) = 17.1°

Common mistakes

Confusing path difference (a distance) with phase difference (an angle or fraction of a cycle) — the two are related but not identical. Forgetting that total internal reflection can only occur when light travels from a denser to a less dense medium, and only beyond the critical angle. Using the wrong form of the photoelectric equation, or forgetting that below the threshold frequency no photoelectrons are emitted regardless of intensity. Treating de Broglie wavelength as applicable only to electrons — the relationship λ = h/p applies to any particle with momentum.

Quick revision checklist

• Define amplitude, frequency, period, speed, wavelength and use v = fλ.
• Distinguish longitudinal and transverse waves, and interpret standing-wave graphs (nodes, antinodes).
• Describe CORE PRACTICAL 4 (speed of sound) and CORE PRACTICAL 5 (string/wire vibration).
• Use v = √(T/µ) and I = P/A.
• Apply Snell’s law, calculate critical angle, and predict total internal reflection.
• Explain diffraction using Huygens’ construction and use nλ = dsinθ (CORE PRACTICAL 6).
• Use the de Broglie equation λ = h/p.
• Use E = hf and hf = φ + ½mv²max for the photoelectric effect, and explain its significance for wave-particle duality.
• Explain atomic line spectra in terms of energy-level transitions.

Related resources

• Unit 2: Electric Circuits — the next sub-topic, completing Unit 2
• Unit 1: Mechanics — the previous unit
• Pearson Edexcel International A Level Physics hub

This guide is intended to support, not replace, engagement with the official Pearson Edexcel specification and your own teacher’s guidance. Always check the current version of the specification for authoritative detail.