Light as Information

Section 2 of 9

The Electromagnetic Spectrum

Part 2: The Electromagnetic Spectrum

Unit convention: we use CGS units throughout (cm, s, erg, K). For convenience, optical/UV wavelengths are often written in nm, where $1\ \text{nm} = 10^{-7}\ \text{cm}$ .

Light as a Wave

Light is an electromagnetic wave — oscillating electric and magnetic fields that propagate through space at a constant speed.

Side-by-side comparison: left shows a simple sine wave labeled 'Mechanical Wave' with wavelength marked; right shows an EM wave with perpendicular electric and magnetic field components. — Figure 1Mechanical waves need a medium (water, air); EM waves don't. Light travels through the vacuum of space - no medium required.JWST/STScI

Unlike mechanical waves (water ripples, sound, a vibrating string), electromagnetic waves don’t need a medium. A water wave is the water moving up and down; a sound wave is air molecules compressing and expanding. But light travels perfectly well through the vacuum of space — what’s oscillating are the electric and magnetic fields themselves.

Both wave types share the same vocabulary:

Wavelength ( $\lambda$ ): the distance between successive crests. For light, wavelengths range from kilometers (radio) down to sub-atomic scales (gamma rays).
Frequency ( $\nu$ ): the number of oscillations per second, in s $^{-1}$ (Hertz, Hz).
Speed ( $c$ ): in vacuum, all electromagnetic waves travel at $c = 2.998 \times 10^{10}\ \text{cm/s}$ .

Nanometer

A unit of length, $1\ \mathrm{nm} = 10^{-9}\ \mathrm{m} = 10^{-7}\ \mathrm{cm}$ — roughly ten hydrogen-atom diameters, and the natural unit for optical and UV light. Visible light spans about 400-700 nm.

Optical and UV wavelengths are often written in nanometers. These three quantities are related by the fundamental wave equation:

All EM waves travel at the same speed $c$ in vacuum; they differ only in how they trade off wavelength against frequency. Since $c$ is constant, the two are inversely related, $\nu \propto \lambda^{-1}$ : long wavelength means low frequency, short wavelength means high frequency.

Problem

Using $\nu = c\lambda^{-1}$ : (1) if wavelength doubles, frequency does what? (2) If frequency triples, wavelength does what? (3) Radio waves have $\lambda \sim 1$ cm; visible light $\lambda \sim 5\times10^{-5}$ cm. How do their frequencies compare?

The Spectrum: From Radio to Gamma

The electromagnetic spectrum spans an enormous range of wavelengths, divided into named bands:

Horizontal electromagnetic spectrum diagram showing a wavelength scale from very short gamma rays (~1e-13 cm) through X-ray and ultraviolet to visible light (expanded as a rainbow, 400-700 nm), then infrared, microwave, and radio up to long wavelengths (~1e3 cm). — Figure 2The EM spectrum spans from gamma rays (about 10^-13 cm) to radio waves (about 10^3 cm). Visible light is a tiny sliver - 400 to 700 nm. Different wavelengths = different physics revealed.JWST/STScI

Band	Wavelength Range	What It Reveals
Radio	$>1$ cm	Cold gas, magnetic fields, pulsars
Microwave	$0.1$ – $1$ cm	CMB, molecular clouds
Infrared	$700$ nm– $0.1$ cm	Warm dust, cool stars, exoplanets
Visible	$400$ – $700$ nm	Stellar surfaces, nebulae
Ultraviolet	$10$ – $400$ nm	Hot stars, active galactic nuclei
X-ray	$0.01$ – $10$ nm	Million-degree plasma, accretion disks
Gamma	shorter than $0.01$ nm	Extreme events: supernovae, GRBs

Key insight: different wavelengths reveal different physics. A galaxy looks completely different in radio versus X-rays because you’re seeing different physical components — cold gas versus hot plasma. This is why astronomers build telescopes for every part of the spectrum.

EM spectrum with astronomical objects shown at each band: gamma rays from black holes and supernovae, X-rays from hot stellar coronae, UV from hot stars, visible from stellar surfaces, infrared from dust and cool stars, microwave from CMB, radio from cold gas and pulsars. — Figure 3Different wavelengths reveal different cosmic phenomena. Gamma rays see black holes; X-rays see hot plasma; visible shows stars; infrared penetrates dust; radio maps cold gas.JWST/STScI

Light as Particles: Photon Energy

Light also behaves as particles called photons. Each photon carries a discrete amount of energy:

Here $h = 6.626 \times 10^{-27}$ erg·s is Planck’s constant. The energy depends on either frequency or wavelength (they’re linked by $c = \lambda\nu$ ). The story: $E \propto \lambda^{-1}$ — shorter wavelength means higher energy, which is why gamma rays can damage DNA while radio waves pass harmlessly through your body.

Visible spectrum from UV through infrared showing a wave pattern with wavelength scale across visible light (400-700 nm). Left side labeled 'higher energy (shorter wavelength)' with compressed waves; right side labeled 'lower energy (longer wavelength)' with stretched waves. — Figure 4Short wavelength = high energy = high frequency. The wave crests are closer together for blue/UV light than for red/IR light. E = hc/lambda quantifies this.JWST/STScI

Problem

Using $E = hc\lambda^{-1}$ : (1) if wavelength doubles, photon energy does what? (2) If wavelength is halved? (3) A 200 nm photon versus an 800 nm photon — how do their energies compare?

Pause & Predict

Same atmosphere, same sunlight - what's different? Commit to a guess before Part 3.

Why do you think the sky looks blue during the day but red/orange at sunset?

Part 3 answers this with Rayleigh scattering.