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Cambridge O Level Physics: Waves (5054)

Study guide to Waves for Cambridge O Level Physics 5054: wave properties, light, lenses, the electromagnetic spectrum and sound, with worked examples.

Subject
Physics
Level
O LEVELS
Topic
Waves
Author
Marlbridge Academic Team
Updated
Reviewed by
Hassan (what this means)

Aligned to Cambridge O Level Physics (5054), 2026-2028. Official specification .

Syllabus page (what it covers and how it is assessed): Cambridge O Level Physics.

Syllabus points this page covers

5054

  • 3.1 General properties of waves
  • 3.2 Light
  • 3.3 Electromagnetic spectrum
  • 3.4 Sound

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This guide works through topic 3, Waves, from the Cambridge O Level Physics 5054 syllabus (examined in 2026, 2027 and 2028), following the syllabus order. The syllabus does not mark any of it as extension content.

Companion pages: revision notes and practice questions. Also see the Physics course hub, a topic checklist and our free diagnostics.

What this guide covers

Sections 3.1 to 3.4: wave properties, light, the electromagnetic spectrum and sound. The lens, eye and radiation-use outcomes are briefest.

3.1 General properties of waves

Waves carry energy from place to place, and no matter is carried along. A cork floating on a pond rises and falls as ripples go by, yet it stays where it is. In a rope or spring, shaking one end sends a pulse along it while each part only moves a short way and returns.

Wave features and definitions

  • Wavefront: a line joining points at the same stage of vibration, such as a line along a crest.
  • Crest (peak) and trough: the highest and lowest points of a transverse wave.
  • Wavelength λ: the distance between two consecutive, identical points, such as two consecutive crests. Unit: metre, m.
  • Frequency f: the number of wavelengths that pass a point per unit time. Unit: hertz, Hz (waves per second).
  • Amplitude: the maximum distance from the mean position.
  • Wave speed v: the distance the wave travels per unit time, in m/s.

The wave equation links them:

v = f × λ

Period T (time for one wave) is 1/f.

Worked example 1. A paddle makes water waves at 4 Hz with crests 0.15 m apart. v = fλ = 4 × 0.15 = 0.60 m/s, and the time between crests is T = 1/4 = 0.25 s.

A sine graph of displacement against distance marks wavelength between two crests (0.40 m) and amplitude from rest position to crest. With f = 5 Hz, v = f x wavelength = 2.0 m/s and the period is 0.2 s.
Wavelength is crest to crest; amplitude is from the middle to a crest; v = f x wavelength.

Transverse and longitudinal waves

In a transverse wave, the vibration direction is at right angles to the direction of energy transfer. Examples: electromagnetic radiation, surface water waves and seismic S-waves (secondary).

In a longitudinal wave the vibration is parallel to the direction of energy transfer. Examples: sound waves and seismic P-waves (primary).

A rope wave moves points up and down at right angles to travel (transverse). A spring wave moves coils back and forth along the direction of travel (longitudinal), bunching into compressions and spreading into rarefactions (Extended names).
Transverse waves vibrate at right angles to the direction of travel; longitudinal waves vibrate along it.
Two cross-sections of the Earth with an earthquake at the top. S-waves travel in straight lines through the mantle but stop at the liquid core, leaving a shadow zone on the far side where no S-waves arrive. P-waves pass through the core and change direction at its boundary.
S-waves cannot cross the liquid core, but P-waves can, which is evidence that part of the core is liquid.

Reflection, refraction and diffraction

  • Reflection at a plane surface: the wave bounces back; wavelength and speed do not change.
  • Refraction: the wave changes direction because its speed changes. The frequency stays the same, so from v = fλ the wavelength changes with the speed.
  • Diffraction through a gap: the wave spreads out after passing through the gap. Spreading is strongest for a gap close to one wavelength wide, and weak for a gap far wider than the wavelength. A longer wavelength diffracts more through the same gap.
  • Diffraction at an edge: waves bend round the edge into the shadow. A longer wavelength bends round more.
Top view of wavefronts meeting a barrier with a gap. With a gap of five wavelengths the wavefronts stay mostly straight and bend only at the edges. With a gap of one wavelength they spread as nearly circular arcs. Diffraction is appreciable only when wavelength and gap are comparable.
A gap about one wavelength wide spreads waves strongly; a wide gap hardly does.
Three rays in a glass semicircle: below the critical angle some light leaves, at 41.8 degrees the refracted ray runs along the surface, above it all light is reflected. sin c = 1/n (Extended).
Above the critical angle all the light is reflected back inside the glass.

The ripple tank

A ripple tank is a shallow tray of water lit from above, so wavefronts show as lines on a screen below.

  • Reflection: a straight barrier returns the wavefronts at the same angle to the barrier.
  • Refraction: a submerged plate makes a shallow region. The waves travel more slowly over the plate, so the wavefronts bunch closer and turn.
  • Diffraction at a gap: narrowing it towards one wavelength spreads the waves more.
  • Diffraction at an edge: wavefronts curve round the end of a barrier.

Worked example 2. In a ripple tank at 10 Hz the wavelength is 3.0 cm in deep water and 1.2 cm in shallow water. Deep: v = 10 × 0.030 = 0.30 m/s. Shallow: v = 10 × 0.012 = 0.12 m/s. The frequency is unchanged and the wave is slower in the shallow region.

Top view of a ripple tank at 10 Hz. Wavefronts cross from deep water (wavelength 3.0 cm, speed 0.30 m/s) to a shallow plate (1.2 cm, 0.12 m/s). The wavefronts bunch up and the ray turns towards the normal from 40 degrees to 14.9 degrees.
Over the plate the wave is slower and its wavelength shorter, at the same frequency.
Top view of a ripple tank. Straight wavefronts reflect from a straight barrier and leave at the same 30 degrees on the other side. In a second panel the wavefronts curve round the edge of a barrier into the shadow region.
In a ripple tank a straight barrier returns wavefronts at equal angles, and waves bend round an edge into the shadow.
Two side views of ripples a quarter period apart. The crest moves right by a quarter wavelength but a floating cork stays at the same horizontal position and only moves up and down.
The wave moves along but the water only vibrates.

3.2 Light

3.2.1 Reflection of light

The normal is a line drawn at right angles to the surface where the ray meets it. The angle of incidence is between the incident ray and the normal. The angle of reflection is between the reflected ray and the normal. The law of reflection says the two angles are equal.

The image in a plane mirror is the same size as the object, as far behind the mirror as the object stands in front of it, and virtual (it cannot be projected onto a screen).

Experiment: the law of reflection. Stand a mirror upright on paper, draw its line and a normal, and shine a narrow ray at a chosen angle. Mark points on the reflected ray, remove the mirror, join the points and measure both angles from the normal.

Experiment: the plane mirror image. Sight two pins in line with the image of an object pin from two positions and draw the lines back behind the mirror. They cross at the image. Measure the distances to the mirror.

Worked example 3. A ray makes 35° with a mirror surface, so i = 55° and the rays are 110° apart.

3.2.2 Refraction of light

Light changes direction when it crosses a boundary and its speed changes. The angle of incidence i is in the first medium and the angle of refraction r in the second, both measured from the normal. Light entering a denser medium slows and bends towards the normal.

The refractive index n of a material is

n = sin i / sin r

(i in air or vacuum, r in the material).

Experiment: refraction by blocks. Draw round a block on paper, shine a ray in at several angles, mark the entering and leaving rays, remove the block and join the points. A rectangular block gives an emergent ray parallel to the incident ray but shifted sideways. A triangular prism bends the ray towards its base.

Worked example 4. A ray in air meets water at an angle of incidence of 50°. n for water is 1.33. Find r.

  1. sin r = sin 50° / 1.33 = 0.766 / 1.33 = 0.576.
  2. r = 35° (35.2°).

Critical angle and total internal reflection. Light passing out of a denser medium into a less dense one bends away from the normal. As i increases, a value is reached where the refracted ray travels along the boundary. That i is the critical angle c. Above that angle every bit of light stays in the denser medium, which is total internal reflection. Use

n = 1 / sin c

Conditions: light going from the denser to the less dense medium, and the angle of incidence greater than c.

Worked example 5. A plastic has c = 42° in air, so n = 1/sin 42° = 1.49. For a glass with n = 1.6, sin c = 1/1.6 = 0.625, so c = 38.7°.

Experiment. Send a ray through the curved face of a semicircular block, aimed at the centre of the flat face, and increase the angle. At first there is a refracted ray and a weak internally reflected ray. At c the refracted ray runs along the flat face. Beyond c only the reflected ray remains.

Optical fibres. A fibre is a thin glass or plastic strand in which light is totally internally reflected from wall to wall. In telecommunications, light pulses carry telephone and internet signals. Advantages over copper cable: more information per second and no electrical interference.

3.2.3 Thin lenses

A thin converging lens makes a parallel beam converge to the principal focus (focal point) F. A thin diverging lens spreads a parallel beam out, as if from a focal point on the incoming side. The principal axis is the line through the centre of the lens at right angles to it. The focal length is the distance from the lens centre to F.

To build a ray diagram, take a ray leaving the top of the object parallel to the principal axis (it passes through the principal focus after the lens) and a ray through the centre of the lens (it carries straight on). Where they meet is the top of the image. For a converging lens:

Object position Image formed
Further than 2F Inverted, real, diminished
Between F and 2F Inverted, real, magnified
Closer than F Upright, virtual, magnified

A real image is formed by converging rays. A virtual image is formed by diverging rays that only appear to come from it. A diverging lens always gives a virtual, upright, smaller image.

A magnifying glass is a converging lens with the object inside F, giving a virtual, upright, enlarged image.

linear magnification = image length / object length

Worked example 6: 1.6 cm object, 4.0 cm image, magnification 4.0/1.6 = 2.5.

The eye. A normal eye focuses light from the object on the retina. A short-sighted eye focuses distant light in front of the retina; a diverging lens corrects it. A long-sighted eye focuses near light behind the retina; a converging lens corrects it.

Ray diagram for a converging lens with f = 4 cm. A 2 cm object 6 cm from the lens gives a real, inverted image 4 cm tall 12 cm beyond the lens, magnified by 2.0.
An object between F and 2F gives a real, inverted, magnified image.
Parallel rays meet at the principal focus after a converging lens. After a diverging lens they spread out and appear to come from a principal focus on the incoming side.
A converging lens brings parallel rays to a focus; a diverging lens spreads them as if from a focus.
To-scale ray diagram with f = 120 and object at 300: image forms at 200, real, inverted and diminished.
An object beyond 2F gives a real, inverted, diminished image.
Ray diagram for a convex lens with the object inside the principal focus. The two refracted rays spread out and never meet; dotted lines traced backwards meet 7.5 cm from the lens on the same side as the object, giving a virtual, upright image 5 cm tall, which is 2.5 times larger than the 2 cm object.
Inside the principal focus a convex lens gives a larger, upright, virtual image.
Ray diagram for a concave lens. A ray parallel to the axis bends away from the axis, appearing to come from the principal focus on the object side; the ray through the centre is undeviated. The refracted rays never cross, but dotted lines traced back meet 4 cm from the lens on the object side, giving a virtual, upright image 1 cm tall (one third of the object).
A concave lens only ever makes a virtual, upright, smaller image.
Four schematic eyes in two rows. Long sight: rays from a near object focus behind the retina, and a convex lens in front of the eye brings them to a focus on the retina. Short sight: parallel rays from a distant object focus in front of the retina, and a concave lens in front of the eye moves the focus back onto the retina.
A convex lens corrects long sight and a concave lens corrects short sight.

3.2.4 Dispersion of light

White light is a mixture of colours. A glass prism refracts each colour by a different amount, so white light spreads into a spectrum. In order of increasing frequency the seven colours are red, orange, yellow, green, blue, indigo, violet. In order of increasing wavelength the order is reversed. Violet bends most and red least.

A ray reflects from a mirror with i and r both 55 degrees measured from the normal, with two marked points on the reflected ray. A second panel shows pins lined up with the image of an object pin; the lines drawn back behind the mirror cross at the image, the same distance behind as the object is in front.
Both mirror practicals: measure i and r from the normal, and find the image where lines from the pins cross behind the mirror.
Three views of a ray aimed at the centre of a semicircular block (n = 1.6) at 25 degrees, 38.7 degrees and 55 degrees. At 25 degrees the ray refracts out, at the critical angle it runs along the flat face, and at 55 degrees it is totally internally reflected.
Increase the angle and the refracted ray bends away until it runs along the face at the critical angle, then only reflection remains.
A ray hits a plane mirror at 35 degrees to the normal and reflects at 35 degrees on the other side. The 55 degree angle to the mirror surface is marked as the common wrong measurement.
Angle of incidence equals angle of reflection, both measured from the normal.
An upright object O is 3.5 m from a vertical plane mirror. Two rays from its base reflect so that angle of incidence equals angle of reflection (36.9 and 24.2 degrees), measured from dashed normals. Dashed extensions behind the mirror meet at the image I, 3.5 m behind the mirror: virtual, upright and the same size.
Two rays from O reflect with i = r and their backward extensions meet at the virtual image I, as far behind the mirror as O is in front.
A ray at 45 degrees in air bends towards the normal to 28 degrees in glass (n = 1.5) and leaves parallel, bending away. n = sin i / sin r = 1.50 (Extended).
Light slows and bends towards the normal entering glass, and speeds up and bends away leaving it.
Wavefronts meet an air-glass boundary at 45 degrees. In air (3.00e8 m/s) they are 545 nm apart; in glass (2.00e8 m/s) 364 nm apart, with the same frequency 5.50e14 Hz. The end entering first slows first, so the ray bends towards the normal to 28.1 degrees. n = 3.00/2.00 = 1.50.
Wavefronts bunch closer in the slower medium, so the ray pivots towards the normal while frequency stays fixed.
A ray in a fibre of n = 1.48 meets the wall at 60 degrees, above the 42.5 degree critical angle, and is totally internally reflected again and again. Uses are endoscopes and communications. A 2.0 km fibre gives a transit time of 9.9 microseconds.
Light zigzags along a fibre by total internal reflection because it meets the wall above the critical angle.
White light enters a glass prism and is refracted at both faces. Red is bent least and violet most, in the order red, orange, yellow, green, blue, indigo, violet. The spread is exaggerated for clarity.
White light splits into a spectrum because violet is bent more than red.

3.3 Electromagnetic spectrum

In order of increasing frequency (and decreasing wavelength): radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays. In a vacuum every one of them moves at 3.0 × 10⁸ m/s, and air changes this very little.

Worked example 7: a 100 MHz (1.0 × 10⁸ Hz) radio signal has λ = v/f = 3.0 × 10⁸ / 1.0 × 10⁸ = 3.0 m.

  • Radio waves: radio and television, astronomy.
  • Microwaves: satellite television, mobile phones, Bluetooth, microwave ovens.
  • Infrared: household electrical appliances, remote controllers, intruder alarms, thermal imaging, optical fibres.
  • Visible light: photography, vision.
  • Ultraviolet: security marking, detecting counterfeit bank notes, sterilising water.
  • X-rays: medical imaging, security scanners, killing cancerous cells, finding cracks in metal.
  • Gamma rays: detecting and killing cancerous cells, sterilising food and medical equipment, finding cracks in metal.

Damage. Too much exposure to microwaves and infrared heats soft tissue and can cause burns. Ultraviolet (skin cancer, cataracts), X-rays and gamma rays (cell mutation, cancer) are ionising.

Seven bands from radio to gamma with their uses. Microwaves and infrared heat tissue and can burn; ultraviolet, X-rays and gamma rays are ionising and can cause cancer or cell mutation.
Each band has its own uses; microwaves and infrared heat, while ultraviolet, X-rays and gamma rays are ionising.
Seven regions from radio to gamma, each with a wave of shorter wavelength than the one above (illustrative) and one use. All travel at 3.0 x 10^8 m/s in a vacuum (Extended).
Frequency rises and wavelength falls from radio waves to gamma rays.

3.4 Sound

Sound is produced by a vibrating source, such as a tuning fork or a drum skin, which pushes on the air next to it.

Sound is a longitudinal wave. A compression is a region where particles are squeezed close and pressure is high; a rarefaction is where they are spaced out and pressure is low. Humans hear about 20 Hz to 20 000 Hz.

Sound needs particles to vibrate, so it cannot travel through a vacuum. Experiment: pump the air out of a jar containing a ringing bell. The sound fades although you still see the hammer strike.

  • Loudness depends on amplitude: larger amplitude, louder sound.
  • Pitch depends on frequency: higher frequency, higher pitch.
  • Timbre (quality): two instruments playing the same note at the same loudness give different trace shapes on an oscilloscope.

An echo is a reflection of sound. To show reflection, direct sound down a tube towards a hard board and find the angle at which a second tube picks up the loudest echo.

Speed of sound. In air it is approximately 330–350 m/s. In general sound is fastest in solids, then liquids, then gases.

Method for the speed of sound in air. Measure the distance d to a large wall. Clap and time the interval t from the clap to the echo with a stopwatch. The sound travels 2d, so v = 2d/t. Repeat and average.

Worked example 8: 85 m to a wall and an echo after 0.50 s gives v = 2 × 85 / 0.50 = 340 m/s.

Ultrasound is sound with a frequency above 20 kHz. Uses: cleaning (vibrations loosen dirt in a bath), prenatal and other medical scanning (echoes from tissue boundaries build a picture) and sonar. For sonar, depth = v × t / 2.

Worked example 9: a sonar pulse returns after 0.08 s in water where v = 1500 m/s, so depth = 1500 × 0.08 / 2 = 60 m.

Two bell jars each with a bell. With air in the jar sound spreads out and is heard. With the air pumped out the hammer still strikes but no sound is heard, because sound needs particles.
Pump the air out of the jar and the bell is still seen ringing but can no longer be heard.

Common errors

  • Saying a wave carries matter with it; only energy is carried.
  • Taking angles from the surface of a mirror or block when they belong to the normal.
  • Saying total internal reflection can happen from air into glass.
  • Saying the frequency changes when a wave refracts. The speed and wavelength change.

Frequently asked questions

Does a wave carry matter? No. A wave transfers energy without carrying matter with it; the particles of the medium only vibrate about fixed positions.

Does frequency change when a wave refracts? No. When a wave refracts, its speed and wavelength change but its frequency stays the same.

Can total internal reflection happen when light goes from air into glass? No. Total internal reflection only happens when light travels from a denser material to a less dense one, such as glass to air, at an angle of incidence greater than the critical angle.

Where should angles of incidence and refraction be measured from? Measure them from the normal, a line at right angles to the surface, not from the surface of the mirror or block.

Official syllabus

Source: topic 3, Waves, of the Cambridge International Education O Level Physics 5054 syllabus for 2026 to 2028.

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