The Electromagnetic Spectrum

6 min read Updated Mar 26, 2026

Your microwave heats leftovers. A radio tower broadcasts to your car. A hospital X-ray images your broken wrist. Your phone uses gigahertz signals to talk to a cell tower. The sun warms your face with infrared.

These look like completely different technologies — but they’re all the same thing: electromagnetic (EM) waves traveling at the speed of light. The only difference between a radio wave and a gamma ray is the wavelength.

That single fact is the punch of this section. Once you internalize that the entire electromagnetic spectrum is just one phenomenon at different wavelengths, the rest of optics — and a lot of biology, chemistry, and medical imaging — clicks into place.

What Are Electromagnetic Waves?

An EM wave is a pair of oscillating fields — one electric, one magnetic — that travel together through space at right angles to each other and to the direction of motion. Neither field needs a medium to oscillate in. Unlike sound (which requires air or water or some material), light can cross the vacuum of space — which is how sunlight reaches Earth across 93 million miles of nothing.

Key properties of all EM waves:

They are transverse waves (oscillation perpendicular to propagation).
The electric and magnetic fields are perpendicular to each other.
They travel at the speed of light in vacuum: $c = 3 \times 10^8$ m/s.
They do not require a medium — they can travel through vacuum.
They carry energy and can transfer it to matter (think solar panels, X-ray exposure, sunburns).

The Fundamental Equation

This one equation tells you everything about the trade-off between frequency and wavelength. Double the frequency, halve the wavelength. Know one, you know the other.

The Spectrum: From Low Energy to High Energy

Full electromagnetic spectrum showing radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and γ rays arranged by increasing frequency and decreasing wavelength — The electromagnetic spectrum. From radio waves (longest wavelength, lowest energy) to γ rays (shortest wavelength, highest energy). All EM waves travel at $c$ in vacuum. The visible band is a tiny sliver of the full spectrum. *Credit: Wikimedia Commons, CC BY-SA*

The EM spectrum arranged from longest wavelength to shortest:

Region	Wavelength range	Frequency range	Common use
Radio	> 1 m	< $3 \times 10^8$ Hz	AM/FM radio, TV, broadcast
Microwave	1 mm – 1 m	$3 \times 10^8$ – $3 \times 10^{11}$ Hz	Microwave ovens, cell phones, WiFi
Infrared (IR)	700 nm – 1 mm	up to $4.3 \times 10^{14}$ Hz	Heat sensing, remote controls
Visible	400 – 700 nm	$4.3 \times 10^{14}$ – $7.5 \times 10^{14}$ Hz	Human vision
Ultraviolet (UV)	10 – 400 nm	up to $3 \times 10^{16}$ Hz	Sunburn, sterilization
X-ray	0.01 – 10 nm	up to $3 \times 10^{19}$ Hz	Medical imaging
Gamma (γ)	< 0.01 nm	> $3 \times 10^{19}$ Hz	Nuclear decay, cancer treatment

The Energy Relationship

Higher frequency → higher energy per photon. This determines how EM radiation interacts with matter:

Radio waves pass harmlessly through your body — too low-energy to break bonds.
Microwaves make water molecules rotate, generating heat (that’s how a microwave oven works).
Visible light excites electrons in retinal pigments → vision.
UV light can break chemical bonds in DNA → mutations and sunburn.
X-rays penetrate soft tissue but get absorbed by dense bone → medical imaging contrast.
Gamma rays can destroy cells → used in radiation therapy for tumors.

The reason UV is dangerous and visible light isn’t comes down to one fact: UV photons carry enough energy to break covalent bonds in DNA. Visible photons don’t. That’s why a sunburn happens from UV exposure even though visible light from the sun is way more intense — it’s about the energy per photon, not total energy delivered.

Speed of Light in Different Media

In vacuum, all EM waves travel at exactly $c = 3 \times 10^8$ m/s. In a material medium (glass, water, air), light slows down. The amount it slows depends on the material’s index of refraction, covered in §8.4. For now:

Light is fastest in vacuum.
Light slows down in matter.
Frequency stays the same when light enters a new medium; wavelength changes (since $v$ changes and $f$ doesn’t).

A radio station broadcasts at 100 MHz. What is the wavelength of the signal?

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3 m.

\lambda = c/f = (3 \times 10^8)/(100 \times 10^6) = 3

m. Radio waves have long wavelengths — this one is about the length of a car. That's why radio antennas tend to be large.

Rank from lowest to highest energy per photon: visible light, γ rays, microwaves, X-rays.

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microwaves < visible < X-rays < γ rays. Energy increases with frequency. Microwaves have the lowest frequency of the four; γ rays have the highest. Use the "Raging Martians" mnemonic ordering.

Visible green light has a wavelength of 550 nm. What is its frequency?

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$\sim 5.5 \times 10^{14}$ Hz.

f = c/\lambda = (3 \times 10^8)/(550 \times 10^{-9}) \approx 5.5 \times 10^{14}

Hz. Visible light frequencies sit in the hundreds of trillions of Hz range — much higher than radio or microwave, much lower than UV/X-ray.