# Waves and Particle Nature of Light

> Edexcel International A-Level Physics · Edexcel IAL Physics Unit 2
> Source: https://www.owlsprep.com/study/edexcel-ial-physics-u2-waves-and-particle-nature-of/

This guide covers all Edexcel IAL Physics Unit 2 content for wave properties, refraction, diffraction, the photoelectric effect, wave-particle duality, and the three required core practicals for this sub-topic.

**Prerequisites:** [Basic algebra and graph interpretation for physics problems](https://www.owlsprep.com/study/edexcel-ial-physics-maths-skills/); [Fundamental SI units and prefixes for physical quantities](https://www.owlsprep.com/study/edexcel-ial-physics-units-prefixes/)

## Learning objectives

- Calculate wave properties using $v=fλ$, $v=√(T/µ)$ and $I=P/A$
- Distinguish between transverse and longitudinal waves, interpret standing wave graphs
- Apply Snell's law, calculate critical angle and predict total internal reflection
- Solve diffraction grating problems using $nλ=dsinθ$, complete core practical calculations
- Use the photoelectric equation $hf=φ+½mv_{max}^2$ and convert between joules and electronvolts
- Explain wave-particle duality for light and electrons, interpret atomic line spectra transitions

## Fundamental Wave Properties and Standing Waves

Waves transfer energy without transferring matter, and are classified as transverse (oscillations perpendicular to direction of travel, e.g. EM waves, string waves) or longitudinal (oscillations parallel to direction of travel, e.g. sound waves, via pressure variations in a medium).

**Standing Wave** — A wave formed by the superposition of two coherent waves of equal amplitude and frequency travelling in opposite directions, with fixed nodes (points of zero displacement) and antinodes (points of maximum displacement). The distance between two adjacent nodes is $λ/2$.

**Worked example:** A guitar string of mass per unit length 0.002 kg m⁻¹ is held under tension of 80 N. It vibrates at its first harmonic frequency of 256 Hz. Calculate the wavelength of the wave on the string.

1. Step 1: Calculate the speed of the wave on the string using $v=√(T/µ)$

   $$v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{80}{0.002}} = \sqrt{40000} = 200 \text{ m s}^{-1}$$
2. Step 2: Rearrange $v=fλ$ to solve for wavelength

   $$\lambda = \frac{v}{f} = \frac{200}{256} = 0.781 \text{ m (3 s.f.)}$$

> **tip**
>
> For Core Practical 5 (vibrating string), measure the length of 10 half-loops and divide by 10 to find the length of one half-loop, then double it to get wavelength, reducing percentage uncertainty.

For Core Practical 4 (speed of sound), use a resonance tube and tuning fork of known frequency to find the wavelength of sound waves, then calculate speed using $v=fλ$. Sound waves are longitudinal, so their standing waves have pressure nodes/antinodes instead of displacement nodes/antinodes.

> **Exam tip:** Exam questions often ask to label nodes and antinodes on standing wave diagrams for both strings and sound waves in closed/open pipes.

## Refraction, Diffraction and Polarisation

**Refractive Index (n)** — Ratio of the speed of light in a vacuum ($c=3×10^8$ m s⁻¹) to the speed of light in a medium ($v$), given by $n=c/v$. Higher refractive index means slower wave speed in the medium.

**Worked example:** Light travels from glass (n=1.52) into air. Calculate the critical angle for the glass-air boundary, and state what happens if light hits the boundary at an angle of incidence of 45°.

1. Step 1: Use the critical angle formula $sinC=1/n$ for a boundary between a denser medium (glass) and rarer medium (air)

   $$sinC = \frac{1}{1.52} = 0.6579$$
2. Step 2: Calculate the critical angle

   $$C = arcsin(0.6579) = 41.1^{\circ} (3 s.f.)$$
3. Step 3: Compare the angle of incidence to the critical angle: 45° > 41.1°, so total internal reflection (TIR) occurs, and all light is reflected back into the glass.

Only transverse waves can be plane polarised, meaning oscillations are restricted to a single plane perpendicular to the direction of travel. Polaroid filters block unpolarised light by only allowing oscillations in one plane to pass, used in sunglasses to reduce glare.

**Worked example:** A diffraction grating has 300 lines per mm. Monochromatic light of wavelength 589 nm is incident normally on the grating. Calculate the angle of the second order maximum.

1. Step 1: Calculate the grating spacing $d$, the distance between adjacent slits, in metres

   $$d = \frac{1}{300 \times 10^3 \text{ lines per m}} = 3.333 \times 10^{-6} \text{ m}$$
2. Step 2: Rearrange the diffraction grating formula $nλ=dsinθ$ to solve for $sinθ$

   $$sinθ = \frac{nλ}{d} = \frac{2 \times 589 \times 10^{-9}}{3.333 \times 10^{-6}} = 0.3534$$
3. Step 3: Calculate the angle of the maximum

   $$θ = arcsin(0.3534) = 20.7^{\circ} (3 s.f.)$$

> **warning**
>
> For Core Practical 6 (wavelength via diffraction grating), measure angles for multiple orders of maximum to calculate a mean value for wavelength, reducing random uncertainty.

> **Exam tip:** Always measure angles from the normal to the boundary in refraction and diffraction questions, never from the boundary surface itself.

## Wave-Particle Duality and Quantum Phenomena

**Photon** — A discrete quantum of electromagnetic radiation, with energy proportional to its frequency, given by $E=hf$. Light travels as photons, which behave as particles in interactions with matter.

**Worked example:** A metal has a work function of 2.3 eV. Ultraviolet light of frequency $1.2×10^{15}$ Hz is incident on the metal. Calculate the maximum kinetic energy of emitted photoelectrons, in eV.

1. Step 1: Calculate the energy of the incident photon in joules

   $$E = hf = (6.63 \times 10^{-34}) \times (1.2 \times 10^{15}) = 7.956 \times 10^{-19} \text{ J}$$
2. Step 2: Convert photon energy from joules to eV

   $$E = \frac{7.956 \times 10^{-19}}{1.60 \times 10^{-19}} = 4.97 \text{ eV}$$
3. Step 3: Use the photoelectric equation $hf = φ + KE_{max}$ to find maximum kinetic energy

   $$KE_{max} = 4.97 - 2.3 = 2.67 \text{ eV (3 s.f.)}$$

Matter also exhibits wave-particle duality: the de Broglie wavelength of a moving particle is given by $λ=h/p$, where $p$ is the momentum of the particle ($p=mv$). Electron diffraction experiments provide evidence for the wave nature of electrons, as diffraction is a wave property.

Atomic line spectra are produced when electrons transition between discrete energy levels in an atom. When an electron falls from a higher energy level $E_2$ to a lower energy level $E_1$, it emits a photon of energy $hf = E_2 - E_1$, producing a line of specific frequency in the emission spectrum.

**Check your understanding**

1. Which of the following provides evidence for the particle nature of light?

   - Electron diffraction
   - Photoelectric effect
   - Diffraction grating patterns
   - Polarisation of light

   *Why:* The photoelectric effect demonstrates that light travels as discrete photons (particles) that transfer energy one-to-one to photoelectrons. The other options provide evidence for the wave nature of light or matter.

> **Exam tip:** You must be able to explain three observations of the photoelectric effect that cannot be explained by the wave model of light: 1) No emission below threshold frequency, 2) Maximum KE of photoelectrons depends only on frequency, not intensity, 3) Emission is instantaneous.

## Common pitfalls

- **Wrong:** Using frequency in kHz or wavelength in nm without converting to SI units in calculations
  - Why it fails: All standard physics formulae require base SI units (Hz for frequency, m for wavelength) to produce correct values for speed, energy and other quantities.
  - Correct: Always convert all given values to base SI units before substituting into formulae, unless explicitly instructed otherwise by the question.
- **Wrong:** Stating that a path difference of $λ$ corresponds to a phase difference of $π$ radians
  - Why it fails: One full wavelength path difference equals one full cycle of oscillation, which is a phase difference of $2π$ radians.
  - Correct: Use the relationship: phase difference (rad) = $\frac{2π \times \text{path difference}}{λ}$ for coherent waves.
- **Wrong:** Assuming that increasing the intensity of incident light increases the maximum kinetic energy of photoelectrons
  - Why it fails: Maximum kinetic energy of photoelectrons depends only on the frequency of incident light, not intensity; intensity only increases the number of photoelectrons emitted if frequency is above the threshold frequency.
  - Correct: Use the photoelectric equation $hf=φ+½mv_{max}^2$ to calculate maximum KE, which has no dependence on light intensity.
- **Wrong:** Calculating diffraction grating spacing $d$ directly as lines per mm, rather than $1/(lines per m)$
  - Why it fails: $d$ is the distance between adjacent slits in metres, so lines per mm must be converted to lines per m before taking the reciprocal to avoid unit errors.
  - Correct: For a grating with $N$ lines per mm, $d = \frac{1}{N \times 10^3} \text{ m}$.
- **Wrong:** Stating that longitudinal waves (like sound) can be plane polarised
  - Why it fails: Polarisation requires oscillations to be restricted to a plane perpendicular to the direction of travel, which is only possible for transverse waves.
  - Correct: Only transverse waves (including all electromagnetic waves) can be polarised; longitudinal waves cannot.

## Cheatsheet

| Concept | Formula | Key Notes |
| --- | --- | --- |
| Wave speed | $v=fλ$ | f in Hz, λ in m, v in m s⁻¹ |
| String wave speed | $v=\sqrt{\frac{T}{µ}}$ | T = tension (N), µ = mass per unit length (kg m⁻¹) |
| Snell's Law | $n_1sinθ_1 = n_2sinθ_2$ | θ measured from normal to boundary |
| Critical angle | $sinC = \frac{1}{n}$ | Only for light moving from denser to rarer medium |
| Diffraction grating | $nλ = dsinθ$ | n = order of maximum, d = grating spacing (m) |
| Photon energy | $E=hf=\frac{hc}{λ}$ | h = Planck's constant, c = speed of light |
| Photoelectric effect | $hf = φ + ½mv_{max}^2$ | φ = work function, $½mv^2$ = max KE of photoelectrons |
| De Broglie wavelength | $λ = \frac{h}{p}$ | p = momentum of particle = mv |
| Intensity | $I = \frac{P}{A}$ | P = power (W), A = area (m²) |

## What's next

Now that you have mastered the waves and particle nature of light content for Edexcel IAL Physics Unit 2, you are ready to move on to the electricity content in Unit 2 Topic 2, which covers current, resistance, circuits and potential dividers. This sub-topic makes up 50% of the content for your WPH12 Unit 2 exam, so make sure you practice past paper questions regularly, focusing on both numerical calculations and explanation questions for quantum phenomena like the photoelectric effect. Pay special attention to the core practicals, as they make up ~15% of the marks for each Unit 2 paper. You should also revise graph interpretation skills for photoelectric effect graphs (KE vs frequency, stopping potential vs frequency) and standing wave graphs, as these are frequently tested. After completing Unit 2 content, you can progress to Unit 4 and Unit 5 content for your full A Level qualification.

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