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Waves

IGCSE Physics 0625 · Unit 3 revision notes

How waves carry energy without matter: wave properties, reflection, refraction, lenses, the electromagnetic spectrum and sound.

37 definitions to learn word for word, 10 equations in their own column, 21 diagrams and graphs. Read it, cover it, test yourself.

3.1a Describing waves
3.1b Reflection, refraction and diffraction of waves
3.2a Reflection of light
3.2b Refraction of light
3.2c Total internal reflection and optical fibres
3.2d Thin lenses
3.2e Dispersion of light
3.3a The electromagnetic spectrum
3.3b Communication and signals
3.4a Sound waves
3.4b Speed of sound, echoes and ultrasound

Definitions (mark-scheme wording)EquationsExam trapsExtended = Extended tier only

3.1aDescribing waves

Definitions

Wavelength (λ): the distance between a point on one wave and the equivalent point on the next wave (e.g. crest to crest).
Amplitude: the maximum displacement of a point on the wave from its rest (undisturbed) position.
Frequency (f): the number of complete waves passing a point per second.
Wave speed: the distance travelled by a wavefront per unit time.
Wavefront: a line joining points on a wave that are in step, e.g. along a crest.
Transverse wave: a wave in which the vibrations are perpendicular to the direction of energy transfer.
Longitudinal wave: a wave in which the vibrations are parallel to the direction of energy transfer.

Key points

Waves transfer energy without transferring matter: the medium only vibrates about a fixed position.
Demonstrate with ropes, slinky springs and a ripple tank.
Highest point = crest (peak); lowest point = trough.
Transverse examples: all electromagnetic waves, water ripples, seismic S-waves.
Longitudinal examples: sound, seismic P-waves.
Frequency is set by the source; it does not change when the wave enters a new medium.

Transverse wave: wavelength is crest to crest; amplitude is from the rest position to a crest or trough.

Longitudinal wave: particles vibrate along the direction of travel, making compressions and rarefactions; λ is compression to compression.

Watch out!

Amplitude is rest position to crest, not crest to trough (that is twice the amplitude).
Wavelength must be measured between equivalent points: crest to crest, not crest to trough.

3.1bReflection, refraction and diffraction of waves

Definitions

Reflection: the change in direction of a wave when it bounces off a surface.
Refraction: the change in direction of a wave when it changes speed on passing from one medium into another.
Diffraction: the spreading out of a wave as it passes through a gap or around the edge of an obstacle.

Key points

Ripple tank: reflection at a straight barrier; refraction where the water gets shallower; diffraction through a gap and at an edge.
Waves slow down in shallow water: wavelength gets shorter and the wavefronts change direction.
In refraction, frequency stays the same; speed and wavelength change together.
In reflection and diffraction the speed, frequency and wavelength are all unchanged.
Extended diffraction is greatest when the gap width is similar to the wavelength; a wide gap gives little spreading.
Extended at an edge, a longer wavelength diffracts (bends round) more.
Extended sound (λ about 1 m) diffracts round doorways; light (λ below 1 µm) does not noticeably.

Refraction in a ripple tank: in shallow water the waves slow down, so the wavefronts are closer together and bend towards the normal.

Extended: diffraction. A gap about one wavelength wide spreads the waves into semicircles; a wide gap lets them through almost straight.

Watch out!

Diffraction does not change the wavelength; draw the spread wavefronts with the same spacing.
Refraction does not change the frequency; only speed and wavelength change.

3.2aReflection of light

Definitions

Normal: a line at 90° to the surface at the point where the ray meets it.
Angle of incidence: the angle between the incident ray and the normal.
Angle of reflection: the angle between the reflected ray and the normal.
Law of reflection: the angle of incidence equals the angle of reflection.
Virtual image: an image that cannot be formed on a screen; the rays only appear to come from it.

Key points

Plane-mirror image: same size, upright, virtual, laterally inverted (left-right swapped).
The image is as far behind the mirror as the object is in front.
Experiment: ray box, plane mirror and protractor; mark the rays, draw the normal, measure i and r.
Extended to locate an image, extend reflected rays backwards behind the mirror (dashed) until they meet.
Extended use i = r to draw accurate ray diagrams and calculate angles.

Law of reflection: i = r, both measured from the normal, never from the mirror surface.

Extended: the image is found where the reflected rays, traced back (dashed), meet: as far behind the mirror as the object is in front.

Watch out!

Angles are measured from the normal: a ray at 30° to the mirror has i = 60°.
A plane-mirror image is virtual; it cannot be caught on a screen.

3.2bRefraction of light

Definitions

Refraction of light: the change in direction of light as it passes from one medium into another, caused by a change in speed.
Angle of refraction: the angle between the refracted ray and the normal.
Refractive index (n): Extended the ratio of the speeds of a wave in two different regions (e.g. speed of light in air / speed in glass).

Key points

Into a denser medium (air to glass) light slows down and bends towards the normal.
Out of a denser medium it speeds up and bends away from the normal.
A ray along the normal (i = 0) passes straight through, but still changes speed.
Frequency is unchanged; the wavelength is shorter in glass.
Experiment: ray box and rectangular glass block; trace rays, draw normals, measure i and r; repeat with semicircular and triangular blocks.
Through a parallel-sided block the emerging ray is parallel to the incident ray (shifted sideways).
Extended plot sin i against sin r; the gradient of the straight line is n.

Rectangular glass block: bends towards the normal on entry, away on exit; the emerging ray is parallel to the incident ray.

Extended: sin i against sin r gives a straight line through the origin; gradient = refractive index n.

Watch out!

Extended: in n = sin i / sin r, i is the angle in air (the less dense medium).
Speed changes at the boundary even when the ray does not bend (i = 0).

3.2cTotal internal reflection and optical fibres

Definitions

Critical angle (c): the angle of incidence in the denser medium for which the angle of refraction is 90°.
Total internal reflection: the complete reflection of light at a boundary when the angle of incidence in the denser medium is greater than the critical angle.

Key points

TIR needs light travelling from a denser to a less dense medium (glass to air) and i > c.
At i = c the refracted ray grazes along the surface (angle of refraction 90°).
Critical angle of glass is about 42°.
Below c the light mostly refracts out, but some is internally reflected (a weak partial reflection).
Experiment: aim a ray at the centre of the flat face of a semicircular block through its curved side; increase i until TIR.
Optical fibres carry light by repeated TIR.
Extended optical fibres are used in telecommunications (internet, phone, cable TV) and medical endoscopes.
45° glass prisms use TIR in periscopes and bicycle reflectors.
Extended a higher refractive index gives a smaller critical angle.

Glass to air: below c the ray escapes; at c it grazes the surface; above c it is totally internally reflected.

Optical fibre: light hits the wall at more than the critical angle every time, so it is totally internally reflected all the way along.

Watch out!

TIR cannot happen going into a denser medium (air to glass).
c is measured from the normal inside the glass, like every other angle.

3.2dThin lenses

Definitions

Principal axis: the line through the centre of the lens at right angles to it.
Principal focus (F): the point where rays parallel to the principal axis meet after passing through a converging lens (or appear to come from, for a diverging lens).
Focal length (f): the distance from the centre of the lens to the principal focus.
Real image: an image formed where rays actually meet; it can be shown on a screen.

Key points

Converging (convex) lens brings parallel rays to F; diverging (concave) lens spreads them out.
Ray rules: parallel to the axis → through F; through the centre → straight on; through F → parallel.
Object beyond 2F: image real, inverted, diminished (camera, eye).
Object between F and 2F: image real, inverted, enlarged (projector).
Describe an image by size, way up, and real or virtual.
Extended object closer than F: image virtual, upright, enlarged; the lens is a magnifying glass.
Extended short sight is corrected with a diverging lens; long sight with a converging lens.

Converging lens, object beyond 2F: the three rays meet to form a real, inverted, diminished image.

Extended: magnifying glass. Object inside F; the rays diverge, and traced back (dashed) they give a virtual, upright, enlarged image.

Diverging lens: parallel rays spread out as if they came from the principal focus F on the same side.

Watch out!

Extended: a converging lens can give a virtual image too, when the object is inside F.
Draw rays with a ruler and stop them at the lens line, not at the curved surface.

3.2eDispersion of light

Definitions

Dispersion: the splitting of white light into its colours because each colour is refracted by a different amount.
Monochromatic light: Extended light of a single frequency (one colour).

Key points

White light is a mixture of colours; a glass prism separates them into a spectrum.
Order: red, orange, yellow, green, blue, indigo, violet.
Red to violet: frequency increases, wavelength decreases.
Violet is refracted most (slowed most in glass); red is refracted least.

Dispersion by a prism: violet bends the most and red the least, spreading white light into a spectrum.

Watch out!

The prism does not add colour; it only separates colours already in white light.

3.3aThe electromagnetic spectrum

Definitions

Electromagnetic wave: a transverse wave that can travel through a vacuum; all electromagnetic waves travel at the same high speed in a vacuum.
Electromagnetic spectrum: the family of electromagnetic waves arranged in order of frequency (or wavelength).

Key points

Order of increasing frequency (decreasing wavelength): radio, microwaves, infrared, visible, ultraviolet, X-rays, gamma.
All EM waves are transverse, transfer energy, and travel at the same speed in a vacuum.
Radio: radio and TV broadcasting, astronomy, RFID. Microwaves: satellite TV, mobile phones, microwave ovens.
Infrared: remote controls, thermal imaging, grills, intruder alarms, optical fibres. Visible: vision, photography, illumination.
Ultraviolet: security marking, detecting fake bank notes, sterilising water. X-rays: medical imaging, airport security.
Gamma: sterilising food and medical equipment, detecting and treating cancer.
Harm: microwaves cause internal heating; infrared causes skin burns; UV damages surface cells and eyes (skin cancer).
X-rays and gamma are ionising: they cause cell mutation and cancer.
Satellite communication is mainly by microwaves: some satellite phones use low orbit satellites; other satellite phones and direct broadcast satellite TV use geostationary satellites.

The EM spectrum: radio has the longest wavelength and lowest frequency, gamma the shortest wavelength and highest frequency.

Watch out!

Gamma rays are not faster than radio waves; all EM waves have the same speed in a vacuum.
Learn the order both ways: by frequency and by wavelength.

3.3bCommunication and signals Extended

Definitions

Analogue signal: a signal that varies continuously and can take any value.
Digital signal: a signal that has only a few discrete values, usually two (0 and 1, off and on).

Key points

Microwaves: mobile phones and wireless internet (pass through walls, need only short aerials).
Radio waves: Bluetooth (pass through walls but are weakened).
Visible light and infrared in optical fibres: cable TV and high-speed broadband (glass is transparent to them).
Sound can be sent as an analogue or a digital signal.
Digital benefits: regenerated exactly, so noise is removed and the range is increased; faster transmission and more data.

Analogue signals vary smoothly and can take any value; digital signals jump between just two values, 0 and 1.

Digital signals pick up noise, but a regenerator restores the clean 0s and 1s; analogue noise cannot be removed.

Watch out!

Regeneration works for digital signals only; amplifying an analogue signal amplifies the noise too.

3.4aSound waves

Definitions

Sound: a longitudinal wave produced by a vibrating source.
Pitch: how high or low a sound is; it depends on the frequency.
Loudness: how loud a sound is; it depends on the amplitude.
Compression: Extended a region of a longitudinal wave where the particles are closer together (higher pressure).
Rarefaction: Extended a region of a longitudinal wave where the particles are further apart (lower pressure).

Key points

Sound is made by vibrating objects and travels as a longitudinal wave.
Sound needs a medium; it cannot travel through a vacuum (bell-in-a-jar experiment).
Human audible range: 20 Hz to 20 000 Hz (20 kHz).
Larger amplitude → louder; higher frequency → higher pitch.
On an oscilloscope trace, taller waves = louder; more waves on the screen = higher pitch.
Extended sound is a series of compressions and rarefactions travelling through the medium.

Oscilloscope traces: a louder sound has a bigger amplitude; a higher-pitched sound has more waves in the same time.

Bell in a jar: as the air is pumped out the bell is still seen vibrating, but the sound fades. Sound needs a medium.

Watch out!

Pitch depends on frequency, loudness on amplitude; do not swap them.
Sound is longitudinal: the air particles vibrate along the direction of travel, they do not travel with the wave.

3.4bSpeed of sound, echoes and ultrasound

Definitions

Echo: a reflected sound wave.
Ultrasound: sound with a frequency higher than 20 kHz (above the range of human hearing).

Key points

Speed of sound in air is about 330-350 m/s.
Measure it outdoors: two people 100 m or more apart; time from seeing a clap or flash to hearing it; v = d/t.
Echo method: clap at a wall; the sound travels there and back, so the distance is 2d.
Extended sound is fastest in solids, slower in liquids and slowest in gases.
Extended ultrasound partly reflects at boundaries between materials; the echo time gives the distance.
Extended uses of ultrasound: non-destructive testing of materials, medical scanning of soft tissue, sonar.

Echo: the sound goes to the wall and back, a total distance of 2d, so v = 2d / t.

Extended: sonar. An ultrasound pulse reflects off the seabed; depth d = vt / 2.

Watch out!

In echo questions divide by 2: the time measured is for the return journey.
Ultrasound is still sound (longitudinal, needs a medium); it is not an EM wave.