🌈Chapter 4 — Electromagnetic Spectrum

DSE Physics · Pan Lloyds Pre-DSE Physics · Electromagnetic Waves & Spectrum

🌊4.1 Nature of Electromagnetic Waves

What Is an Electromagnetic Wave?

An electromagnetic wave (EM wave) is a wave composed of oscillating electric and magnetic fields that are mutually perpendicular and propagate together through space at the speed of light.

📌 Three defining properties of EM waves:

They are transverse waves — both the electric field E and the magnetic field B are perpendicular to the direction of propagation.
They do not require a medium and can travel through a vacuum — this is how sunlight reaches Earth across empty space.
In a vacuum they travel at the speed of light: c ≈ 3 × 10⁸ m·s⁻¹.

Figure 4-1 — In an electromagnetic wave the electric field E (red) and the magnetic field B (blue) oscillate perpendicular to each other and to the direction of travel.

Fundamental Wave Quantities

v = f × λ (wave speed = frequency × wavelength)

For all electromagnetic waves travelling in a vacuum, v = c, so we may write:

c = f × λ ⟹ λ = c / f

📌 Important inverse relationship: Higher frequency f ⟹ shorter wavelength λ ⟹ higher photon energy E.

Photon Energy

Electromagnetic energy is transferred in discrete packets called photons. The energy carried by a single photon is given by the Planck–Einstein relation:

E = h × f = (h × c) / λ

where h is Planck's constant, h ≈ 6.63 × 10⁻³⁴ J·s.

🌈4.2 The Visible Spectrum

Newton's Prism Experiment

In 1666, Sir Isaac Newton passed a beam of white light through a glass triangular prism and showed that it spread out into a band of seven colours. This demonstrated that white light is not a single entity but a mixture of different colours, each with its own wavelength.

Figure 4-2 — White light entering a glass prism is dispersed into the seven visible colours.

The Seven Colours of Visible Light

Colour	English Name	Wavelength Range (nm)	Frequency Property
🔴 Red	Red	620 – 750	Lowest frequency, longest wavelength
🟠 Orange	Orange	590 – 620	—
🟡 Yellow	Yellow	570 – 590	—
🟢 Green	Green	495 – 570	—
🔵 Blue	Blue	450 – 495	—
🟣 Indigo	Indigo	425 – 450	—
🟪 Violet	Violet	380 – 425	Highest frequency, shortest wavelength

💡 Memory aid: The classic mnemonic "ROY G. BIV" — Red, Orange, Yellow, Green, Blue, Indigo, Violet — lists the colours in order from longest to shortest wavelength.

⚠️ Why dispersion occurs — different refractive indices:

Red light has a smaller refractive index → it is deviated the least from its original path.
Violet light has a larger refractive index → it is deviated the most.
This wavelength-dependent bending is exactly why a prism separates white light into a spectrum.

Formation of a Rainbow

When sunlight enters a raindrop, three optical processes take place in sequence:

First refraction at the air–water interface — white light is dispersed into the seven colours.
Total internal reflection at the back surface of the raindrop.
Second refraction as the light exits the droplet back into the air.

Because red light bends less than violet light, the colours emerge at different angles, producing the familiar arc of a rainbow.

🌌4.3 Beyond Visible Light

The Complete Electromagnetic Spectrum

The full electromagnetic spectrum, arranged from longest to shortest wavelength, covers seven major regions plus the highest-energy cosmic rays:

Figure 4-3 — The complete electromagnetic spectrum, from radio waves to cosmic rays.

Detailed Comparison of the Seven Regions

Region	Wavelength Range	Frequency	Typical Source	Typical Applications
Radio waves	> 1 mm	Lowest	Oscillating circuits, antennas	AM/FM broadcasting, television, wireless networks
Microwaves	1 mm – 1 m	Low	Magnetron tubes, antennas	Microwave ovens, radar, satellite communications, WiFi
Infrared (IR)	700 nm – 1 mm	Moderate–low	Warm objects, the Sun	Night-vision devices, IR remote controls, thermometers
Visible light	380 – 750 nm	Moderate	The Sun, light bulbs, flames	Illumination, vision, optical-fibre communication
Ultraviolet (UV)	10 – 380 nm	Moderate–high	The Sun, mercury-vapour lamps	Sterilisation, counterfeit detection, vitamin-D synthesis
X-rays	0.01 – 10 nm	High	X-ray tubes, electron impacts on metal targets	Medical imaging, airport security screening
Gamma rays (γ)	< 0.01 nm	Highest	Radioactive nuclei, nuclear reactions	Cancer radiotherapy, sterilisation of medical equipment

💡 Remember the trend: Moving from left to right across the spectrum, wavelength decreases, frequency increases, and photon energy increases. The shorter the wavelength, the more biologically hazardous the radiation tends to be.

📡4.4 Applications of the EM Spectrum

Radio Waves

Application scenarios

📻 AM/FM broadcasting — wavelengths of several hundred metres carry audio signals to receivers.
📺 Television transmission — VHF/UHF bands carry video and audio.
📱 Mobile communications — 4G and 5G cellular networks.
🛰️ Satellite communication — long-range radio links between ground stations and orbiters.
🎮 Bluetooth and WiFi — note these actually fall in the microwave region.

Microwaves

Application scenarios

🍿 Microwave ovens: water molecules absorb microwave energy, vibrate violently, and the resulting friction heats the food from within.
🛩️ Radar systems: short microwave pulses are emitted and the reflected signal is used to detect aircraft, ships, and weather patterns.
🛰️ Satellite links: microwaves carry signals between Earth stations and communication satellites.
📶 WiFi: routers transmit at 2.4 GHz and 5 GHz, both within the microwave band.

Infrared (IR)

Application scenarios

📺 IR remote controls — modulated infrared pulses command televisions and air-conditioners.
🌃 Night-vision devices — detect thermal IR emitted by warm objects.
🌡️ Infrared thermometers — measure body temperature (e.g. forehead thermometers).
📡 Optical-fibre communication — infrared light carries data through glass fibres with low loss.

Ultraviolet (UV)

Application scenarios

🌞 Sunlight exposure: UV-B triggers synthesis of vitamin D in the skin.
🧴 Sterilisation lamps: UV-C damages the DNA of bacteria and viruses, killing or inactivating them.
💵 Counterfeit detection: UV light reveals hidden security features on banknotes.
💎 Fluorescence: certain materials absorb UV photons and re-emit the energy as visible light.

⚠️ Excessive UV exposure is harmful: it can cause sunburn, premature skin ageing, skin cancer, and cataracts. Broad-spectrum sunscreen and UV-blocking sunglasses provide effective protection.

X-rays

Application scenarios

🏥 Medical radiography: because bone absorbs X-rays more strongly than soft tissue, internal fractures and lung conditions become visible on a film or digital detector.
🛂 Security screening: airport scanners inspect luggage for concealed objects.
🔬 Crystallography: X-ray diffraction reveals the atomic-scale structure of crystals and biomolecules.

Gamma Rays (γ)

Application scenarios

🎗️ Cancer radiotherapy: focused gamma beams damage the DNA of malignant cells.
🧴 Sterilisation of medical instruments: gamma irradiation is more thorough than heat-based methods.
🔬 Radioactive tracing: gamma-emitting isotopes track chemical and biological processes.

⚡4.5 Radiation and Energy

Black-body Radiation

Every object above absolute zero emits electromagnetic radiation. As its temperature rises, two key changes occur:

The total radiated power increases dramatically (proportional to T⁴ — the Stefan–Boltzmann law).
The peak emission wavelength shifts to shorter values (Wien's displacement law) — moving from infrared into the visible range.

📝 Worked example — colour of thermal radiation

Iron rod at 500 °C: dull red glow — emission peaks in the infrared.
Iron rod at 800 °C: orange-red glow — visible spectrum begins to dominate.
Iron rod at 1500 °C: incandescent white glow — the full visible spectrum is emitted.
Surface of the Sun (~ 5500 °C): white light with peak intensity in the yellow-green region.

The Solar Spectrum

The Sun is by far the dominant source of electromagnetic radiation reaching Earth:

Visible light (~ 40 %) — what our eyes detect and what drives photosynthesis.
Infrared (~ 50 %) — felt as warmth and responsible for most solar heating.
Ultraviolet (~ 10 %) — small in proportion but biologically significant: causes sunburn and drives vitamin-D synthesis.
All other bands combined contribute a negligible fraction.

Biological Hazards of Electromagnetic Radiation

Region	Energy Level	Main Hazard	Typical Protection
Radio waves, Microwaves	Low	Thermal heating (the microwave-oven effect)	Maintain a safe distance from strong sources
Infrared	Moderate	Skin burns from intense sources	Avoid direct exposure to hot radiant bodies
Visible light	Moderate	Retinal damage from very bright sources	Never look directly at the Sun
Ultraviolet	Moderately high	Sunburn, skin cancer, cataracts	Sunscreen, UV-blocking sunglasses
X-rays	High	Radiation damage, increased cancer risk	Lead shielding
Gamma rays	Highest	Acute radiation sickness, fatality	Thick lead or concrete barriers

⚠️ General rule of thumb: Higher frequency (shorter wavelength) ⟹ greater photon energy ⟹ greater biological hazard ⟹ more difficult to shield.

📌 Chapter Summary

🎯 Five must-remember concepts:

Nature of EM waves: E ⊥ B ⊥ direction of propagation; in vacuum they travel at c ≈ 3 × 10⁸ m·s⁻¹.
Wave relation: c = f × λ — frequency and wavelength are inversely proportional.
Photon energy: E = h × f — higher frequency means higher energy per photon.
Visible spectrum: Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROY G. BIV).
Full spectrum order: Radio → Microwave → Infrared → Visible → Ultraviolet → X-rays → Gamma rays (longest to shortest wavelength).

📝 Key Terms — Bilingual Glossary

English	Chinese	Symbol
Electromagnetic Wave	電磁波	EM wave
Electric Field	電場	E
Magnetic Field	磁場	B
Frequency	頻率	f
Wavelength	波長	λ
Speed of Light	光速	c
Photon	光子	—
Planck's Constant	普朗克常數	h
Infrared	紅外光	IR
Ultraviolet	紫外光	UV
Gamma Ray	伽馬射線	γ

✏️ Quick Quiz — Try It Yourself

Question 1 — What is the approximate wavelength range of visible light?

📌 Click to reveal the answer

Visible light spans roughly 380 nm – 750 nm.

Since 1 nm = 10⁻⁹ m, this corresponds to wavelengths from about 3.8 × 10⁻⁷ m to 7.5 × 10⁻⁷ m.

Question 2 — How does a microwave oven heat food?

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Microwaves at about 2.45 GHz are strongly absorbed by water molecules inside the food. The molecules vibrate violently and the internal friction converts this absorbed energy into heat, cooking the food efficiently from within.

Question 3 — Why does a prism split white light into seven colours?

📌 Click to reveal the answer

The refractive index of glass depends on wavelength:

Red light has a smaller refractive index → it bends less from its original direction.
Violet light has a larger refractive index → it bends more.

Because the seven colours are refracted by different amounts, they emerge from the prism separated in space — producing a spectrum.

Question 4 — Which is more energetic and more dangerous, X-rays or γ-rays?

📌 Click to reveal the answer

γ-rays have the highest frequency, the shortest wavelength and the greatest photon energy, making them the most biologically hazardous form of EM radiation.

General rule: higher frequency ⟹ more energy ⟹ greater hazard ⟹ harder to shield.