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Light & optics

The Electromagnetic Spectrum

Radio waves, heat radiation, the light your eye can see, X-rays and gamma rays are one and the same thing — electromagnetic waves that differ only in their wavelength. Drag along the spectrum below and see how wavelength, frequency and photon energy are related.

Michael Grant  ·  michael.h.grant@gmail.com

A travelling electromagnetic wave: an electric field E (vertical) and a magnetic field B (horizontal) oscillate at right angles to each other — and move forwards at the speed of light.

01 · One wave — many faces

Maxwell unified electricity, magnetism and light in 1865.

When James Clerk Maxwell wrote down his four equations in the 1860s, he discovered that an oscillating electric and magnetic field can break free and travel through empty space as a wave — at a speed that matched exactly the already measured speed of light. The conclusion was astonishing: light is an electromagnetic wave. It later turned out that radio waves, microwaves, infrared, ultraviolet, X-rays and gamma rays are exactly the same kind of wave. The only thing that separates them is the wavelength.

Two simple equations tie the whole spectrum together. The first concerns the geometry of the wave, the second quantum physics — where the energy sits in the photon itself:

c = λ · f speed of light = wavelength × frequency  (c = 2.998·10⁸ m/s)
E = h · f = h·c / λ photon energy = Planck's constant × frequency  (h = 6.626·10⁻³⁴ J·s)

Both say the same thing: short wavelength means high frequency and high energy. That is why a gamma photon carries more than a million million times as much energy as a radio photon — even though both are the same kind of wave. A practical rule of thumb for photons in and around the visible:

E [eV] ≈ 1240 / λ [nm] energy in electronvolts when the wavelength is given in nanometres

02 · Explore the spectrum

Drag the bar — or use the arrow keys — and watch the numbers and the wave change.

Wavelength λ
—
Frequency f
—
Photon energy E
—
Region
—
schematic
← long wave · low energyshort wave · high energy →
visible
The wavelength is roughly the size of —.

03 · The seven regions

From everyday radio signals to the most violent radiation in the universe. Tap a card to jump there in the explorer.

04 · The narrow strip we can see

All visible light fills only a hair-thin slice of the spectrum: about 380–750 nm.

It is a thought-provoking fact: everything our eyes have ever seen — sunsets, rainbows, the starry sky in my eVscope2 — lies in a strip narrower than an octave. The frequency barely doubles from red to violet. Colour is wavelength: long-wave light is seen as red, short-wave as violet.

750 nm 650 550 450 380 nm

Just beyond each end lie the neighbours: infrared (the heat radiation we feel but do not see) on the red side, and ultraviolet (what gives sunburn) on the violet side. Many animals see further in both directions than we do — bees, for example, see into the UV.

05 · Three worked examples

The equations applied to reality.

FM radio. A station broadcasts at a frequency f = 100 MHz = 1.00·10⁸ Hz. The wavelength is λ = c/f = (3.0·10⁸ m/s)/(1.0·10⁸ Hz) = 3.0 m — which is why a simple FM aerial is about 1.5 m long, half a wavelength. This is the radio region.
A green photon. Green light has λ = 550 nm. The energy is E ≈ 1240/550 = 2.25 eV. That is just the order of magnitude of the energy in atoms' electron transitions — which is why atoms emit light in the visible region.
An X-ray photon. With λ = 0.10 nm, E ≈ 1240/0.10 = 12,400 eV = 12.4 keV. The energy is thousands of times greater than the green photon's — which is why X-rays can pass through soft tissue while visible light is stopped.

06 · How the spectrum was discovered

Bit by bit, over a century.

07 · Seeing the universe at every wavelength

The same object tells different stories in different regions.

The atmospheric window

The Earth's atmosphere is transparent only in two broad windows: the visible (with a little near-infrared) and the radio region. That is why my eVscope2 at Marshøj can capture galaxies in visible and near-IR light from the Earth's surface — but ultraviolet, X-rays and gamma rays from space are absorbed by the air and need space telescopes such as Hubble, Chandra and Fermi.

Each wavelength reveals something new: cool dust shines in the infrared (James Webb sees through dust clouds), hot gas around black holes glows in X-rays, and the cosmic microwave background — the oldest light in the universe, cooled to 2.7 K — lies in the microwave region. Multi-wavelength astronomy is the art of putting all these pictures together into one.