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Lesson 5 of 5The Wave Nature of Light
Unit 4 · Lesson 5 of 5

Light as an Electromagnetic Wave

What kind of wave light is and what makes one, the electromagnetic spectrum from radio to gamma rays, why a prism splits colours, why diffraction limits how much detail any lens can see, and the technologies that put all of it to work.

6 min read12 practice questionsAsk AI about this →

Key things to remember

  1. 1Electromagnetic waves are produced by accelerating charges, such as an oscillating electric dipole in an antenna.
  2. 2In a vacuum all electromagnetic waves travel at and obey .
  3. 3Longest to shortest wavelength: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma ray.
  4. 4Dispersion: the refractive index depends on wavelength, so violet bends more than red in glass.
  5. 5Resolution limit: in radians. Bigger openings and shorter wavelengths see finer detail.

The last three topics showed that light interferes, diffracts and polarizes, so it is a transverse wave. That leaves an obvious question: a wave of what? Water waves are moving water and sound is moving air, but light crosses the vacuum of space from the Sun with nothing to move. The answer is that light is a travelling pattern of electric and magnetic fields, and visible light is only a thin slice of a much wider family of waves that includes the signals carrying your phone calls and the X-rays in a dentist's office.

Where electromagnetic waves come from

In the 1860s James Clerk Maxwell combined the laws of electricity and magnetism and found they predicted waves of electric and magnetic field travelling at a speed that matched the measured speed of light. In the late 1880s Heinrich Hertz generated and detected such waves in his laboratory using electric sparks, confirming the prediction. The source of every electromagnetic wave is an accelerating charge. A radio transmitter is the clearest case: an alternating current drives electrons up and down an antenna, making an oscillating electric dipole — the top of the antenna is positive while the bottom is negative, then the reverse, many times a second. The changing electric field around it creates a changing magnetic field, which creates a changing electric field, and the disturbance moves outward at , oscillating at the same frequency as the charges.

restamplitudewavelength λcresttroughAmplitude is measured from the REST position, not trough to crest — that full swing is twice the amplitude.Amplitude carries the energy; for sound it is loudness. Wavelength and frequency set the pitch.
Fig 1An electromagnetic wave has the same anatomy as any wave: the electric field rises and falls with a definite wavelength and amplitude.
Properties shared by every electromagnetic wave
The electric field, the magnetic field and the direction of travel are all perpendicular to one another, so the wave is transverse. In a vacuum every electromagnetic wave travels at , regardless of frequency, and obeys . No medium is needed. The only thing that distinguishes radio from gamma rays is frequency, and therefore wavelength.
BandApproximate wavelengthTypical sourceCommon use
Radiolonger than about Electrons oscillating in an antennaAM and FM broadcasting, communication
Microwaveabout to Electrons oscillating in a magnetron or a small antennaMicrowave ovens, Wi-Fi, radar, cell networks
Infraredabout to Vibrating charges in any warm objectRemote controls, thermal imaging, night vision
Visibleabout (violet) to (red)Electron energy transitions in atoms; very hot objectsVision, lasers, fibre optics
Ultravioletabout to Electron transitions; the SunSterilization, fluorescence
X-rayabout to Fast electrons suddenly stopped in a metal targetMedical and dental imaging, security scanners
Gamma rayshorter than about Changes inside atomic nucleiCancer treatment, sterilizing medical equipment
Band boundaries are approximate and overlap. Wavelength decreases and frequency increases down the table.

Refraction and dispersion

In a material, light slows to , where is the refractive index, and it bends at a boundary according to . The key detail is that is slightly different for each wavelength. In glass and water, violet light travels a little slower than red, so it has a slightly higher and bends more. This spreading of white light into its colours is dispersion: it is how a prism makes a spectrum, and it is half of how a rainbow forms (the other half is reflection inside each raindrop). Refraction also explains a mirage. Air just above a hot road is less dense and has a slightly lower index than the cooler air above it, so light from the sky curves gradually upward toward your eye, and you see an image of the sky on the road that looks like water.

Diffraction limits resolution

Every lens, telescope, camera and pupil is an opening, and light diffracts through openings. A distant point of light therefore never focuses to a perfect point, but to a tiny blurred disc. When two points are so close together that their discs overlap too much, they look like one. The smallest angle between two points that can just be told apart is approximately

D is the diameter of the circular opening. A larger opening or a shorter wavelength resolves finer detail.

Technologies that use the wave nature of light

TechnologyWave propertyHow it works
SpectroscopeDiffraction grating or prism dispersionSpreads light into a spectrum. Each element emits its own set of wavelengths, so the lines identify what a lamp, flame or star is made of.
CDs, DVDs and Blu-ray discsDiffraction and interferenceData is stored in a spiral track of tiny pits. The closely spaced tracks act as a reflection grating, which is why a disc shows rainbow colours.
HologramsInterferenceFilm records the interference pattern between a reference beam and light scattered from an object. Lighting the pattern rebuilds the original wavefronts, so the image has depth. They are hard to copy, so they are used as security features on cards and bank notes.
Polarized lensesPolarization by reflection and filtersVertical transmission axes block horizontally polarized glare from water, snow and roads.
Anti-reflection coatingsThin-film interferenceA quarter-wavelength layer makes the two reflections cancel, so more light is transmitted.
Night visionThe infrared part of the spectrumThermal cameras detect the infrared emitted by warm bodies; image intensifiers amplify the faint light that is present.
Wireless networksMicrowave electromagnetic wavesWi-Fi uses bands near and ; the longer wavelength of the 2.4 GHz band diffracts around obstacles and passes walls more easily.
Why each new disc format holds more
A laser beam cannot be focused to a spot much smaller than its wavelength, because of diffraction. CD players use infrared light () with tracks apart, DVDs use red light () with tracks apart, and Blu-ray uses violet-blue light () with tracks apart. A shorter wavelength makes a smaller spot, so pits and tracks can be packed more closely: the resolution limit, read in reverse, is a data-storage limit.

These technologies have real costs and benefits worth weighing. Fibre-optic cables and wireless networks carry enormous amounts of information and let publications and services move online, which can reduce paper and physical shipping — but data centres and networks consume electricity, and short-lived devices add to electronic waste. Discs are giving way to streaming, which changes where the energy is used rather than removing it. Polarized lenses and anti-reflection coatings improve safety and efficiency for drivers and solar panels. When you assess a technology, name the physics it relies on, then trace its effects on people and on the environment in both directions.

Worked examples

Reveal one step at a time and try to beat it to the next line.

Example 1
An FM station broadcasts at . Find the wavelength of its radio waves.
Example 2
The tracks on a CD are apart, so the disc acts as a reflection grating. White light shines on it. Find the first-order angles for violet () and red () light.
Example 3
White light enters a glass prism at an angle of incidence of . The glass has for red light and for violet light. Find the angle of refraction for each colour.
Example 4
A pupil across views light of wavelength . In ideal conditions, what is the smallest angle it could resolve, and from how far away could the two headlights of a car, apart, just be seen as separate?

Where marks get lost

  • Thinking different electromagnetic waves travel at different speeds in a vacuum. They all travel at ; only frequency and wavelength differ.
  • Forgetting to convert MHz or GHz to hertz before using . and .
  • Saying red light bends more than violet in a prism. Violet has the higher refractive index in glass, so it bends more.
  • Using degrees in . The formula gives radians.
  • Believing a bigger lens gives more diffraction blur. A larger opening gives a smaller minimum angle, so finer detail.

Flashcards 8

What produces electromagnetic waves?
Speed of every electromagnetic wave in a vacuum
The electromagnetic spectrum, longest wavelength first
Dispersion
+ 4 more

Practice

1
A Wi-Fi router transmits at . What is the wavelength of its signal, in centimetres?
cm
2
What is the frequency of green light with wavelength ? Give your answer in units of .
× 10¹⁴ Hz
3
What is the source of all electromagnetic waves?
4
Order these parts of the electromagnetic spectrum from longest wavelength to shortest.
  1. 1Ultraviolet
  2. 2Gamma rays
  3. 3X-rays
  4. 4Radio waves
  5. 5Microwaves
  6. 6Infrared
  7. 7Visible light
5
White light passes through a glass prism. Why is violet light bent more than red light?
6
An AM radio station broadcasts at . What is the wavelength of its signal, in metres?
m
7
Why can a Blu-ray disc hold much more data than a CD of the same size?
8
Match each technology or effect to the wave property it depends on.
Polarized sunglasses
Spectroscope
Anti-reflection coating
Hologram
Mirage on a hot road
9
What is the name for the separation of white light into its colours because the refractive index depends on wavelength?
10
A telescope has a mirror across. What is its minimum resolvable angle for light? Give your answer in units of radians.
× 10⁻⁶ rad
11
A CD held under a lamp shows bands of rainbow colour. What causes them?
12
Light enters glass with a refractive index of . What is its speed in the glass, in units of ?
× 10⁸ m/s

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