Physics › 🔦 Optics & Light

Colour & the Electromagnetic Spectrum

The rainbow you can see is just one thin slice of a wave family that stretches from radio towers to the inside of a nuclear reactor.

High school

💡

The big idea: Light, radio waves, X-rays, and gamma rays are all the same physical thing — oscillating electric and magnetic fields racing through space at the speed of light. What separates them is purely their wavelength (or equivalently, their frequency), and that one number quietly determines everything from what colour we perceive to whether a wave will politely pass through you or knock electrons off your DNA.

🎯 By the end, you'll be able to

Explain what makes red light 'red' and violet light 'violet' in terms of wavelength.
Use the relation f = c/λ to convert between wavelength and frequency for any electromagnetic wave.
Place radio, microwave, infrared, visible, ultraviolet, X-ray, and gamma waves in order and describe a real use and a real risk for each.
Explain, in plain language, why higher-frequency EM waves carry more energy and can be more hazardous to living tissue.

📎 You should already know

Waves: wavelength, frequency, and amplitude
Basic algebra (rearranging a simple equation)
Rough idea of energy as 'the ability to cause change'

A rainbow is a message written in wavelengths

Hold a prism up to sunlight and it fans out into red, orange, yellow, green, blue, violet. Nothing is being added — the prism is simply sorting light that was already a mixture, the way a sieve sorts pebbles by size. Every colour you have ever seen corresponds to a specific \( \lambda \) (wavelength) of light, somewhere between about 400 and 700 nanometres. But visible light is a rounding error. It's a narrow band inside a vastly larger family of waves — radio, microwave, infrared, ultraviolet, X-ray, gamma — that differ from visible light in exactly one respect: how tightly their oscillations are packed together.

🔑 One wave, one speed, one dial to turn

Radio waves, light, and gamma rays are all electromagnetic waves: a self-propagating ripple of electric and magnetic fields. In a vacuum (and to good approximation in air) every single one of them travels at the same speed, \( c \approx 3.00 \times 10^8 \) m/s. Since speed is fixed, wavelength and frequency are locked in a seesaw: stretch the wavelength out and the frequency must drop, squeeze the wavelength down and the frequency must climb. That's the entire spectrum — one dial, wavelength, turned from kilometres down to the width of an atomic nucleus.

\[ c = f\lambda \quad \Longrightarrow \quad f = \dfrac{c}{\lambda} \]

Speed of light c (constant) equals frequency f times wavelength λ. Know any one of f or λ, and you know the other.

\[ E = hf \]

Photon energy E is proportional to frequency f, where h is Planck's constant. Higher frequency (shorter wavelength) always means a more energetic — and potentially more damaging — photon.

🎮 Interactive: Slide across the electromagnetic spectrum LIVE

Drag from radio through to gamma rays and watch wavelength, frequency, and photon energy change together — notice how visible light is a sliver in the middle.

📝 Worked example: Ripe tomato-red light has a wavelength of about 700 nm. What is its frequency?

Convert to metres: \( \lambda = 700\text{ nm} = 700 \times 10^{-9}\text{ m} = 7.00 \times 10^{-7}\text{ m} \)
Rearrange \( c = f\lambda \) to solve for frequency: \( f = \dfrac{c}{\lambda} \)
Plug in numbers: \( f = \dfrac{3.00 \times 10^{8}}{7.00 \times 10^{-7}} \)
Divide: \( 3.00/7.00 = 0.4286 \), and \( 10^{8}/10^{-7} = 10^{15} \)
Combine: \( f = 0.4286 \times 10^{15} = 4.29 \times 10^{14}\text{ Hz} \)

✓ About 4.3 × 10^14 Hz — 430 trillion oscillations every second, just to make something look red.

📝 Worked example: A home WiFi router broadcasts at a frequency of 2.4 GHz. What wavelength is that, and how does it compare to visible light?

Convert to Hz: \( f = 2.4\text{ GHz} = 2.4 \times 10^{9}\text{ Hz} \)
Rearrange \( c = f\lambda \) to solve for wavelength: \( \lambda = \dfrac{c}{f} \)
Plug in numbers: \( \lambda = \dfrac{3.0 \times 10^{8}}{2.4 \times 10^{9}} \)
Divide: \( 3.0/2.4 = 1.25 \), and \( 10^{8}/10^{9} = 10^{-1} \)
Combine: \( \lambda = 1.25 \times 10^{-1}\text{ m} = 0.125\text{ m} = 12.5\text{ cm} \)

✓ 12.5 cm — roughly a hand's width, about 250,000 times longer than a typical wavelength of visible light (around 500 nm).

✨ Same physics, wildly different jobs

Because wavelength sets how a wave interacts with matter, each band of the spectrum ends up doing a completely different job in daily life. Radio waves (centimetres to kilometres) slip through walls and carry broadcast signals and WiFi. Microwaves (centimetres) are absorbed efficiently by water molecules, which is exactly why they cook food and why radar and phone signals use them. Infrared is radiated by anything warm — it's why night-vision goggles and TV remotes work. Visible light is the narrow band your eyes evolved to detect, tuned to the wavelengths the sun puts out most strongly. Ultraviolet carries enough energy to trigger vitamin D production in skin, and enough to damage skin cells with overexposure. X-rays punch through soft tissue but not bone, which is why they're used for imaging. Gamma rays, the shortest wavelength of all, come from the nucleus itself and carry so much energy per photon that they can tear electrons off atoms entirely.

⚠️ Not all photons are equally dangerous

Because \( E = hf \), the danger of an EM wave to living tissue tracks its frequency, not its intensity alone. Radio and microwave photons are low-energy — they can heat tissue if intense enough (think of a microwave oven) but they don't have enough energy per photon to strip electrons from atoms. Ultraviolet, X-ray, and gamma photons are ionizing radiation: energetic enough to knock electrons loose and damage DNA, which is why UV causes sunburn and skin cancer risk, and why X-ray and gamma exposure is carefully limited and shielded in medical and industrial settings.

Check your understanding

1. Which of the following has the longest wavelength?

Radio waves sit at the low-frequency, long-wavelength end of the spectrum — wavelengths can range from centimetres to kilometres, far longer than visible light's few hundred nanometres.

2. Green light has a wavelength of about 500 nm. What is its frequency?

f = c/λ = (3.0 × 10^8 m/s) / (5.0 × 10^-7 m) = 6.0 × 10^14 Hz.

3. Why are X-rays and gamma rays more hazardous to living cells than radio waves, even though all are 'just' electromagnetic waves?

All EM waves travel at the same speed c. What changes is frequency, and E = hf means higher-frequency photons (X-ray, gamma) carry enough energy to ionize atoms and break chemical bonds — radio photons don't.

4. A microwave oven operates around 2.45 GHz and an FM radio station broadcasts around 100 MHz. Which one has the shorter wavelength?

Since λ = c/f, a higher frequency means a shorter wavelength. 2.45 GHz is over 20 times higher frequency than 100 MHz, so the microwave oven's wavelength (about 12 cm) is much shorter than the FM station's (about 3 m).

✅ Key takeaways

Every electromagnetic wave — radio, light, gamma rays — travels at the same speed c, so wavelength and frequency are linked by c = fλ.
Colour is simply the human eye's way of reporting wavelength within the narrow 400–700 nm visible band.
Moving from radio to gamma rays, wavelength shrinks, frequency rises, and photon energy (E = hf) rises with it — which is why each band has a different practical use.
Ionizing bands (UV, X-ray, gamma) carry enough energy per photon to damage DNA, while radio and microwave photons do not, no matter how intense the beam.