Waves and Particle Nature of Light

Q: How do I convert between joules and electronvolts?

Multiply energy in eV by to get joules, or divide energy in joules by the same value to get eV.

Edexcel International A-Level Physics· 2018 Spec Issue 3, Unit 2 (WPH12) Statements 33–63· 45 min read

1. Fundamental Wave Properties and Standing Waves★★☆☆☆⏱ 10 min

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).

📘 Definition

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 $v = \sqrt (T /µ)$
$v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{80}{0.002}} = \sqrt{40000} = 200 \text{ m s}^{-1}$
2
Step 2: Rearrange $v = f λ$ to solve for wavelength
$\lambda = \frac{v}{f} = \frac{200}{256} = 0.781 \text{ m (3 s.f.)}$

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 $v = f λ$ . 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.

2. Refraction, Diffraction and Polarisation★★★☆☆⏱ 12 min

📘 Definition

Refractive Index (n)

Ratio of the speed of light in a vacuum ( $c = 3 \times 1 0^{8}$ 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 $s in C = 1/ n$ 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 $nλ = d s in θ$ to solve for $s in θ$
$sinθ = \frac{nλ}{d} = \frac{2 \times 589 \times 10^{-9}}{3.333 \times 10^{-6}} = 0.3534$
3
Step 3: Calculate the angle of the maximum
$θ = arcsin(0.3534) = 20.7^{\circ} (3 s.f.)$

Exam tip:

Always measure angles from the normal to the boundary in refraction and diffraction questions, never from the boundary surface itself.

3. Wave-Particle Duality and Quantum Phenomena★★★★☆⏱ 15 min

📘 Definition

Photon

A discrete quantum of electromagnetic radiation, with energy proportional to its frequency, given by $E = h f$ . 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 $1.2 \times 1 0^{15}$ 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 $h f = φ + K E_{ma x}$ 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 ( $p = m v$ ). 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 $h f = E_{2} - E_{1}$ , producing a line of specific frequency in the emission spectrum.

✓ Quick check

Which of the following provides evidence for the particle nature of light?
- Electron diffraction
- Photoelectric effect
- Diffraction grating patterns
- Polarisation of light
Reveal answer
Photoelectric effect —
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.

4. Common Pitfalls

Wrong move:

Using frequency in kHz or wavelength in nm without converting to SI units in calculations

Why:

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 move:

Always convert all given values to base SI units before substituting into formulae, unless explicitly instructed otherwise by the question.

Wrong move:

Stating that a path difference of $λ$ corresponds to a phase difference of $π$ radians

Why:

One full wavelength path difference equals one full cycle of oscillation, which is a phase difference of $2 π$ radians.

Correct move:

Use the relationship: phase difference (rad) = $\frac{2 π \times path difference}{λ}$ for coherent waves.

Wrong move:

Assuming that increasing the intensity of incident light increases the maximum kinetic energy of photoelectrons

Why:

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 move:

Use the photoelectric equation $h f = φ + ½ m v_{ma x}^{2}$ to calculate maximum KE, which has no dependence on light intensity.

Wrong move:

Calculating diffraction grating spacing $d$ directly as lines per mm, rather than $1/ (l in es p er m)$

Why:

$d$ 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 move:

For a grating with $N$ lines per mm, $d = \frac{1}{N \times 1 0 ^{3}} m$ .

Wrong move:

Stating that longitudinal waves (like sound) can be plane polarised

Why:

Polarisation requires oscillations to be restricted to a plane perpendicular to the direction of travel, which is only possible for transverse waves.

Correct move:

Only transverse waves (including all electromagnetic waves) can be polarised; longitudinal waves cannot.

5. Quick Reference Cheatsheet

Concept	Formula	Key Notes
Wave speed	$v = f λ$	f in Hz, λ in m, v in m s⁻¹
String wave speed	$v = \frac{T}{µ}$	T = tension (N), µ = mass per unit length (kg m⁻¹)
Snell's Law	$n_{1} s in θ_{1} = n_{2} s in θ_{2}$	θ measured from normal to boundary
Critical angle	$s in C = \frac{1}{n}$	Only for light moving from denser to rarer medium
Diffraction grating	$nλ = d s in θ$	n = order of maximum, d = grating spacing (m)
Photon energy	$E = h f = \frac{h c}{λ}$	h = Planck's constant, c = speed of light
Photoelectric effect	$h f = φ + ½ m v_{ma x}^{2}$	φ = work function, $½ m v^{2}$ = 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)

6. Frequently Asked

Do I need to memorise the double-slit interference formula for this unit?

No, the Edexcel IAL Unit 2 data sheet only includes the diffraction grating formula $nλ = d s in θ$ . Double-slit interference questions will provide any required formula if numerical calculation is needed; you only need to understand the conceptual basis of two-source interference.

Is the photoelectric effect part of AS or A2 content for Edexcel IAL Physics?

It is explicitly part of Unit 2 (IAS/AS Level) content for the 2018 specification, so you will be tested on it in your WPH12 exam, do not defer revision of this content to A2.

How do I convert between joules and electronvolts?

Multiply energy in eV by $1.60 \times 1 0^{- 19} J eV^{- 1}$ to get joules, or divide energy in joules by the same value to get eV.

Going deeper

official_specEdexcel IAL Physics 2018 Specification Unit 2Refer to pages 32-41 for this sub-topic
formula_sheetEdexcel IAL Physics Unit 2 Data SheetAll required formulae for this sub-topic are provided on the exam data sheet

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.