Waves
Summary: Covers transverse and longitudinal waves, the wave equation (v = fλ), reflection, refraction, total internal reflection, diffraction, sound waves, the electromagnetic spectrum (uses and dangers of each type), dispersion of light, and converging lens ray diagrams. This topic combines abstract wave theory with practical optics. Tags: igcse physics waves optics electromagnetic-spectrum sound Created: 2026-07-16 Last Updated: 2026-07-16
Transverse and Longitudinal Waves
Waves transfer energy without transferring matter.
Transverse waves: The vibration/oscillation of particles (or fields) is perpendicular to the direction of wave travel.
- Examples: light, all EM waves, water waves, waves on a string, S-waves (secondary seismic waves)
- Have crests (peaks) and troughs
Longitudinal waves: The vibration/oscillation of particles is parallel to the direction of wave travel.
- Examples: sound, ultrasound, P-waves (primary seismic waves), shock waves
- Have compressions (regions of high pressure, particles close together) and rarefactions (regions of low pressure, particles far apart)
- Require a medium to travel through (cannot travel through a vacuum)
Key terms for all waves:
| Term | Definition |
|---|---|
| Amplitude | Maximum displacement from the rest/equilibrium position |
| Wavelength (λ) | Distance between two consecutive identical points on a wave (e.g., crest to crest) |
| Frequency (f) | Number of complete waves passing a point per second, measured in hertz (Hz) |
| Period (T) | Time for one complete wave to pass a point, T = 1/f |
| Wave speed (v) | Distance travelled by a wave per unit time |
The Wave Equation
wave speed = frequency × wavelength
v = fλ
- v = wave speed (m/s), f = frequency (Hz), λ = wavelength (m)
Example 1: A water wave has a frequency of 5 Hz and a wavelength of 0.4 m. Calculate its speed.
v = fλ = 5 × 0.4 = 2 m/s
Example 2: A radio wave travels at 3.0 × 10⁸ m/s and has a frequency of 100 MHz (100 × 10⁶ Hz). Calculate its wavelength.
λ = v / f = 3.0 × 10⁸ / 100 × 10⁶ = 3.0 × 10⁸ / 1.0 × 10⁸ = 3.0 m
Reflection
When a wave hits a boundary between two media, some or all of it bounces back.
Law of reflection: The angle of incidence equals the angle of reflection (i = r). All angles are measured from the normal — an imaginary line perpendicular to the surface at the point of incidence.
Plane (flat) mirrors:
- Produce a virtual image (cannot be projected onto a screen — light rays appear to come from behind the mirror but do not actually pass through the image)
- Image is the same size as the object
- Image is laterally inverted (left-right reversed)
- Image is the same distance behind the mirror as the object is in front
- Image is upright
Refraction
Refraction is the change in direction of a wave as it passes from one medium to another due to a change in its speed.
Rules of refraction:
- When a wave enters a denser medium (e.g., air → glass): it slows down, and bends towards the normal
- When a wave enters a less dense medium (e.g., glass → air): it speeds up, and bends away from the normal
- If the wave hits the boundary along the normal (angle of incidence = 0°): it does not change direction, but its speed still changes
Refractive index (n) (qualitative for IGCSE):
n = sin i / sin r
Where i = angle in vacuum/air, r = angle in the medium.
Critical Angle and Total Internal Reflection (TIR)
When light travels from a denser medium to a less dense medium (e.g., glass → air):
- At the critical angle (c), the refracted ray travels along the boundary (angle of refraction = 90°)
- For angles of incidence greater than c, total internal reflection occurs — all light is reflected back into the denser medium
Conditions for TIR:
- Light must travel from a denser to a less dense medium
- Angle of incidence must be greater than the critical angle
Relationship: sin c = 1 / n (where n is the refractive index)
Uses of TIR:
- Optical fibres: Light is repeatedly totally internally reflected along the fibre, carrying information. Used in broadband internet, telephone cables, and endoscopes (medical imaging inside the body)
- Prisms in periscopes and binoculars: TIR at 45° in glass prisms (critical angle for glass ≈ 42°) reflects light — more efficient than mirrors
Diffraction
Diffraction is the spreading out of waves after they pass through a gap or around an obstacle.
Factors affecting amount of diffraction:
- Larger wavelength compared to gap size → more diffraction
- Narrower gap compared to wavelength → more diffraction
- When gap width ≈ wavelength → maximum diffraction (waves spread out almost semicircularly)
Sound Waves
Sound waves are longitudinal waves consisting of compressions and rarefactions.
Key facts about sound:
- Sound requires a medium to travel — cannot travel through a vacuum
- Speed of sound: fastest in solids, slower in liquids, slowest in gases (approximately 330-340 m/s in air at room temperature)
- Pitch is determined by frequency: higher frequency = higher pitch
- Loudness is determined by amplitude: larger amplitude = louder sound
- Sound waves reflect to produce echoes (used in sonar, depth sounding)
- Ultrasound: sound waves with frequencies above human hearing (>20,000 Hz)
Uses of ultrasound:
- SONAR (Sound Navigation and Ranging): ultrasound pulses reflected from seabed/shoals of fish; time delay used to calculate distance
- Medical imaging: ultrasound scans of unborn babies, internal organs — safer than X-rays (no ionising radiation)
- Industrial cleaning: high-frequency vibrations dislodge dirt from delicate items
The Electromagnetic Spectrum
All EM waves are transverse waves that travel at the same speed in a vacuum:
c = 3.0 × 10⁸ m/s
The EM Spectrum in order of increasing frequency (and decreasing wavelength):
| Radiation | Wavelength Range (approx.) | Frequency Range (approx.) |
|---|---|---|
| Radio | >0.1 m | <3 × 10⁹ Hz |
| Microwave | 0.001 m to 0.1 m | 3 × 10⁹ to 3 × 10¹¹ Hz |
| Infrared (IR) | 700 nm to 1 mm | 3 × 10¹¹ to 4.3 × 10¹⁴ Hz |
| Visible Light | 400 nm (violet) to 700 nm (red) | 4.3 × 10¹⁴ to 7.5 × 10¹⁴ Hz |
| Ultraviolet (UV) | 10 nm to 400 nm | 7.5 × 10¹⁴ to 3 × 10¹⁶ Hz |
| X-rays | 0.01 nm to 10 nm | 3 × 10¹⁶ to 3 × 10¹⁹ Hz |
| Gamma (γ) | <0.01 nm | >3 × 10¹⁹ Hz |
Mnemonic for EM spectrum order (low to high frequency): Radio, Microwave, Infrared, Visible, UV, X-ray, Gamma.
Uses and Dangers of Each EM Radiation
| Radiation | Uses | Dangers |
|---|---|---|
| Radio | Broadcasting (radio, TV), communications, Wi-Fi, Bluetooth | No known hazards at typical exposure levels |
| Microwave | Satellite communications, mobile phones, cooking (microwave ovens — water molecules absorb microwave energy), radar | Can cause internal heating/burns at high intensity — microwave ovens have metal shields to prevent leakage |
| Infrared | Remote controls, thermal imaging/night vision cameras, heating (radiant heaters, toasters, grills), optical fibre communication | Can cause skin burns at high intensity |
| Visible Light | Seeing, photography, optical fibre communication, photosynthesis in plants | Intense light can damage retina (looking at the Sun or lasers) |
| Ultraviolet | Sunbeds/tanning, security marking (fluorescent inks), detecting forged bank notes, sterilising water/equipment | Skin burns (sunburn), skin cancer, eye damage (cataracts). UV from the Sun is partially blocked by the ozone layer |
| X-rays | Medical imaging (bone fractures, dental X-rays), airport security scanners, industrial inspection of welds/metal parts | Ionising — can cause mutations and cancer. Exposure is minimised by lead shielding, limited dose, staff leaving room during exposure |
| Gamma | Sterilising medical equipment and food (kills bacteria), cancer treatment (radiotherapy — targeted gamma rays kill cancer cells), industrial radiography (detecting cracks in pipes) | Most dangerous — highly ionising, can cause cancer, radiation sickness. Thick lead/concrete shielding needed. Sources handled remotely |
Dispersion of White Light
When white light passes through a triangular glass prism:
- Light is refracted twice (entering and leaving the prism)
- Different colours (wavelengths) are refracted by different amounts — violet is refracted most, red is refracted least
- White light splits into its constituent colours: Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROYGBIV)
This shows that white light is a mixture of all colours of the visible spectrum. Each colour has a different wavelength and frequency but all travel at the same speed in a vacuum.
Lenses — Converging (Convex) Lenses
A converging lens is thickest at the centre. It brings parallel rays of light to a point (the focal point or focus).
Key terms:
- Principal axis: line through the centre of the lens, perpendicular to it
- Focal point (F): the point where rays parallel to the principal axis converge after passing through the lens
- Focal length (f): distance from the centre of the lens to the focal point
- 2F: twice the focal length from the lens centre
- Optical centre: centre of the lens — a ray passing through here is not deviated
Ray Diagrams for Converging Lenses
Draw at least two of these three construction rays:
- A ray parallel to the principal axis → passes through the focal point F on the other side
- A ray passing through the optical centre → continues straight (no deviation)
- A ray passing through F on the object side → emerges parallel to the principal axis
Image Formation Summary
| Object Position | Image Position | Image Characteristics | Real or Virtual? |
|---|---|---|---|
| Beyond 2F | Between F and 2F (other side) | Diminished, inverted | Real |
| At 2F | At 2F (other side) | Same size, inverted | Real |
| Between F and 2F | Beyond 2F (other side) | Magnified, inverted | Real |
| At F | At infinity | — | No image formed (rays emerge parallel) |
| Inside F (closer than F) | On same side as object, behind the lens | Magnified, upright | Virtual |
Real vs Virtual Images:
- Real image: light rays actually converge and pass through the image — can be projected onto a screen (e.g., camera, projector)
- Virtual image: light rays appear to diverge from the image but do not actually pass through it — cannot be projected (e.g., magnifying glass, plane mirror)
Magnification
magnification = image height / object height
Applications of Converging Lenses
| Application | Object Position | Image Details |
|---|---|---|
| Camera | Beyond 2F | Real, diminished, inverted image on film/sensor. Focusing: move lens closer to/further from sensor |
| Projector | Between F and 2F | Real, magnified, inverted image on distant screen. Slide must be inserted upside-down |
| Magnifying glass | Inside F (object closer than F) | Virtual, magnified, upright image on same side as object |
Sources
- BBC Bitesize GCSE Physics — Waves topic, BBC (free educational resource)
- OpenStax College Physics — Waves chapter, Rice University (free, CC BY 4.0)
- Cambridge IGCSE Physics 0625 — Waves section, Cambridge Assessment International Education
- CK-12 Physics for High School — Waves chapter, CK-12 Foundation (free, CC BY-NC 3.0)
Related Notes
- Energy Resources and Transfer — Solar radiation, infrared absorption/emission, solar panels
- Electricity and Magnetism — EM induction links changing magnetic fields and electric fields; electromagnets
- Nuclear Physics — Gamma radiation
- Space Physics — Red shift, CMBR, evidence from EM radiation from space
- IGCSE-Phys-Index — Full IGCSE Physics index
Keywords
transverse, longitudinal, amplitude, wavelength, frequency, wave speed, reflection, refraction, critical angle, total internal reflection, optical fibre, diffraction, ultrasound, electromagnetic spectrum, radio, microwave, infrared, visible light, ultraviolet, X-ray, gamma, converging lens, focal point, real image, virtual image, magnification, dispersion, normal
Common Misconceptions
| Misconception | Reality |
|---|---|
| ”All waves need a medium to travel” | EM waves can travel through a vacuum. Sound waves cannot |
| ”Refraction happens because light bounces off the boundary” | Refraction is due to a change in speed at the boundary. Reflection is bouncing |
| ”The angle of incidence is measured from the surface” | All angles (incidence, reflection, refraction) are measured from the normal — the perpendicular line at the point of incidence |
| ”A virtual image is one that doesn’t exist” | A virtual image exists but light rays only appear to come from it — they don’t actually pass through it. It cannot be projected onto a screen |
| ”Higher frequency means a louder sound” | Frequency determines pitch (high/low). Amplitude determines loudness |
| ”EM waves are ranked by how fast they travel” | All EM waves travel at exactly the same speed in a vacuum (3 × 10⁸ m/s). They differ in frequency and wavelength |
| ”X-rays and gamma rays are the same thing” | They differ in origin — X-rays come from electron transitions, gamma from nuclear decay. They overlap in the EM spectrum but gamma generally has higher frequency |
| ”A magnifying glass produces a real image” | A magnifying glass is used with the object inside F, producing a virtual, magnified, upright image |