The Physics of Light, Wavelength, and Spectrum

The pieces below are usually taught separately: wavelength, photon energy, refractive index, diffraction, photometry, and polarization. In real optical systems they are coupled. This bench lets you push them together and watch the numbers move as one system.

What we call "light" is one stripe in a very wide family of electromagnetic radiation. The whole family obeys the same Maxwell equations and travels through vacuum at the same speed - the speed of light, c ≈ 2.998 × 10⁸ m/s. The differences between radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays are differences of wavelength and frequency, not of fundamental nature.

Three numbers describe a beam of monochromatic light: its wavelength λ (the distance between successive wave crests), its frequency ν (how many crests pass a point per second), and its photon energy E. Two equations link them. The first is Maxwell's: every electromagnetic wave in vacuum travels at the same speed, so wavelength and frequency are inversely related.

The second comes from quantum mechanics. In 1905 Einstein showed (extending Planck's 1900 work on blackbody radiation) that light is exchanged with matter in discrete packets called photons, each carrying an energy proportional to frequency.

Together these say: shorter wavelength → higher frequency → more energy per photon. A violet photon (400 nm) carries roughly 3.10 eV; a red photon (700 nm) carries 1.77 eV - nearly half as much energy. Beyond visible light, an X-ray photon at 0.1 nm carries 12 400 eV - enough to ionize an atom and break chemical bonds.

Out of an electromagnetic family spanning more than 16 orders of magnitude in wavelength, our cones can see roughly one octave - from 380 nanometers (deep violet) to 780 nanometers (deep red). Why exactly this band?

Two evolutionary constraints converged. The sun's emission peaks here. The surface temperature of the sun (~5778 K) produces a blackbody-like spectrum whose maximum output, after atmospheric filtering, sits around 500 nm. Any eye trying to gather useful light on this planet would do best to tune itself to this band. Water absorbs everything else. Our eyes are filled with water and aqueous humor. Water is transparent in the visible band and opaque to most ultraviolet and infrared. So even if photoreceptors could in principle respond to other wavelengths, our optical media throw most of them away.

James Clerk Maxwell showed in 1864 that electric and magnetic fields can sustain each other while propagating through space - producing self-perpetuating transverse waves whose speed, computed from purely electrical and magnetic measurements, exactly matched the known speed of light. The conclusion was unavoidable: light is an electromagnetic wave.

The wave model immediately explains interference, diffraction, and polarization. Two coherent waves that meet in phase reinforce one another and produce a bright spot; out of phase, they cancel. Thomas Young's 1801 double-slit experiment showed this directly with light passing through two narrow slits - and was the strongest argument for the wave theory until quantum mechanics complicated the story.

The wave model could not explain everything. The photoelectric effect - the ejection of electrons when light strikes a metal - depended on the frequency of light, not its intensity. Below a threshold frequency, no electrons came out no matter how bright the light. Above the threshold, even a faint beam ejected them immediately.

In 1905 Einstein proposed that light arrives in discrete energy packets - photons - each with energy E = hν. A photon either has enough energy to liberate an electron or it does not, regardless of how many photons are present. This explained the photoelectric effect, won Einstein the 1921 Nobel Prize, and gave physics back its particle picture of light - which had been Newton's view all along.

So is light a wave or a particle? The honest answer is: neither, exactly. Light is a quantum entity that behaves like a wave in some experiments and like a particle in others. Modern physics regards both pictures as approximate. The full description is the quantum electromagnetic field, in which a photon is an excitation of the field with wave-like statistics and particle-like discrete arrivals.

When light passes from one medium to another - air to glass, water to air - its speed changes, and so its direction bends. The amount of bending is governed by Snell's law:

The index of refraction n of a medium is the ratio of the speed of light in vacuum to its speed in that medium. Vacuum has n = 1; air is essentially 1.0003; water about 1.333; common crown glass 1.52; diamond 2.42. Because n depends slightly on wavelength, different colors bend by different amounts - which is exactly how a prism separates white light into a spectrum.

When light passes through a medium containing small particles, some photons are deflected - scattered - rather than absorbed or transmitted straight through. The physics depends on how the particle size compares to the wavelength of light. Rayleigh scattering applies when particles are much smaller than the wavelength - molecules of N₂ and O₂ in the atmosphere are a classic case. Its intensity scales as 1/λ⁴, which means short wavelengths scatter far more strongly than long ones.

This single fact explains a lot. The midday sky is blue because incoming sunlight scatters from atmospheric molecules, and the short blue wavelengths scatter most strongly in all directions - including toward your eye. The sun itself at midday looks white-yellow because most of its blue light has been scattered out. At sunset, the path through atmosphere is so long that even the longer-wavelength reds eventually scatter, leaving the direct sun a deep orange.

Any object with a temperature above absolute zero emits electromagnetic radiation. A perfect emitter - one that absorbs all incident light and re-radiates only by its temperature - is called a blackbody. Its emission spectrum is described by Planck's law, the formula whose derivation in 1900 launched quantum mechanics.

Two derived laws follow. Wien's displacement law says the peak wavelength shifts as λ_peak = 2898 μm·K / T - hotter objects peak at shorter wavelengths. Stefan-Boltzmann's law says the total power radiated scales as T⁴, so doubling temperature multiplies output by 16.

Physics measures light in radiometric units - watts of total radiant power - that ignore the observer. But human vision is wavelength-selective. A 1-watt source emitting in deep red looks much dimmer than a 1-watt source emitting near 555 nm where cone sensitivity peaks. To talk about visual brightness, we need photometry: radiant power weighted by the photopic luminosity function V(λ).

The constant K_m = 683 lm/W at 555 nm sets the definition of the lumen. A monochromatic green light at 555 nm reaches the maximum possible 683 lm/W. The same wattage at 700 nm yields only about 28 lm/W - the same energy, but visually 24 times dimmer.

A light wave's electric field oscillates transverse to its direction of motion - but the orientation of that oscillation is a separate degree of freedom. Light whose electric field oscillates in one specific direction is linearly polarized. Light whose oscillation orientation is random or rotates over time is unpolarized.

A polarizing filter transmits only the component of the wave whose electric field aligns with the filter's axis. Two polarizers crossed at 90° transmit nothing. This is the principle behind LCD screens, polarized sunglasses, and 3D cinema glasses.

Light from a point source spreads out into a sphere. The same total flux gets distributed over an increasingly large surface area, so the illuminance falling on any patch decreases as 1/r². Doubling the distance quarters the brightness; tenfold the distance, hundredfold the dimming.

Six questions on the physics of light. Wrong answers come with brief explanations.