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LightExtendabout 44 min

Waves, particles and the light you cannot see

Beyond visible light: wave versus particle, a real chocolate-bar experiment, and looking into the past with light-years.

Step past visible light into the wider spectrum, meet the wave-versus-particle debate (light is genuinely both), measure light's speed with a microwave and a chocolate bar, see how bending stretches every day, and use light-years to look into the past.

Start at chapter 1

In this part you’ll

  • Place visible light within the wider electromagnetic spectrum by wavelength.
  • Give at least one piece of evidence each for light behaving as a wave and as a particle.
  • Carry out (or understand) a real measurement of the speed of light using a microwave oven.
  • Explain why atmospheric refraction adds a few minutes of daylight to every day.
  • Use light-years to say how far into the past you are looking at a given astronomical object.

Everything so far has treated light as a ray — a straight arrow that reflects and refracts. That model is enormously useful and completely wrong about what light actually is.

This layer opens the two big questions physicists spent three centuries fighting over: is light a wave, or a stream of particles? (Answer: astonishingly, both, depending on the question you ask.) It also steps past the narrow band of wavelengths your eyes can catch, tries a genuine speed-of-light project with a chocolate bar, and leaves you with open questions nobody has fully answered.

Chapter 01

Beyond what your eyes can see

Visible light — roughly 400 to 700 nanometres — is only a sliver of a vastly wider family called the electromagnetic spectrum. Every member of that family is the same underlying phenomenon (an oscillating electric and magnetic field) travelling at the same speed, c, differing only in wavelength — and therefore in frequency and in energy.

TableThe electromagnetic spectrum, longest wavelength to shortest
BandRoughlyA familiar use
Radiometres to kilometresAM/FM broadcast, mobile phone signals
Microwavemillimetres to centimetresMicrowave ovens, radar, satellite links, Wi-Fi
Infrared700 nm to about 1 mmTV remotes, thermal cameras, the warmth you feel from a fire
Visible light400–700 nanometresEverything in this topic so far
Ultraviolet10–400 nanometresSunburn, sterilising water, some security ink under a UV lamp
X-rays0.01–10 nanometresMedical and dental imaging, airport baggage scanners
Gamma raysunder 0.01 nanometresEmitted by radioactive decay and in cancer radiotherapy

Worked example

0 / 4 steps shown

One wavelength across the whole spectrum: an FM radio station

All India Radio's FM stations broadcast around 100 MHz. Using wavelength = c ÷ frequency, how long is one wave of an FM radio signal, and how does that compare with visible light?

Need a different angle?
TableOne representative wavelength from each band, with its frequency and photon energy, all computed from the same two formulas (f = c ÷ λ and E = hc ÷ λ)
BandWavelengthFrequencyPhoton energy
Radio1 m3.00 × 10⁸ Hz0.0000012 eV
Microwave1 cm3.00 × 10¹⁰ Hz0.00012 eV
Infrared2,000 nm1.50 × 10¹⁴ Hz0.62 eV
Visible (red)700 nm4.28 × 10¹⁴ Hz1.77 eV
Visible (violet)400 nm7.49 × 10¹⁴ Hz3.10 eV
Ultraviolet200 nm1.50 × 10¹⁵ Hz6.2 eV
X-ray0.1 nm3.00 × 10¹⁸ Hz12.4 keV
Gamma ray0.001 nm3.00 × 10²⁰ Hz1,240 keV

Lab

Sort six electromagnetic bands into longer or shorter wavelength than visible light.

Order matters here: sort each electromagnetic band by roughly how long its wavelength is.

6 cards, 2 bins. Tap a card, then tap its bin. You can also drag, or press a bin’s number key.

Text version of this activity

Six electromagnetic bands — radio, microwave, infrared, ultraviolet, X-ray and gamma — sorted by whether their wavelength is longer or shorter than visible light's 400–700 nanometre range. Radio, microwave and infrared sit on the long side; ultraviolet, X-ray and gamma sit on the short side, with visible light as the narrow dividing band in between.

Need a different angle?

Worked example

0 / 4 steps shown

Why X-rays need thick lead aprons and gamma rays need even more shielding

Using the rule E (in eV) = 1240 ÷ wavelength (in nanometres), estimate the energy of a single medical X-ray photon of wavelength 0.1 nm, and compare it with a single green light photon (about 550 nm).

Need a different angle?

Chapter 02

Is light a wave? The case for yes

A wave's calling card is diffraction and interference: waves bend slightly around obstacles and through narrow gaps, and two overlapping waves can reinforce or cancel each other. In 1801, Thomas Young shone light through two narrow, closely spaced slits and saw exactly this — a pattern of bright and dark bands where the light from the two slits alternately reinforced and cancelled. Particles fired through two slits, like tiny bullets, could never do that; only waves interfere.

Worked example

0 / 4 steps shown

A rainbow you can hold: diffraction from a CD

A CD's data track is a spiral of tiny pits spaced about 1.6 micrometres (1.6 × 10⁻⁶ m) apart — closely spaced enough to diffract light noticeably, acting like a reflective diffraction grating. At what angle does green light (550 nm) diffract from a CD's surface, and why does tilting a CD in the light show a rainbow?

Need a different angle?

Lab

Sort six real observations into wave evidence and particle (photon) evidence for the nature of light.

Is this observation best explained by light behaving as a wave, or as a particle (photon)?

6 cards, 2 bins. Tap a card, then tap its bin. You can also drag, or press a bin’s number key.

Text version of this activity

Six genuine physical observations — Young's interference bands, a CD's diffraction rainbow, the photoelectric effect's frequency threshold, a solar cell's instant response, a rainbow's continuous colour smear, and single-photon clicks in a sensitive detector — sorted into whichever picture of light, wave or particle, explains them most naturally. The deliberate lesson of the sort: both bins fill up. No single picture explains every card.

Need a different angle?

Chapter 03

Is light a particle? The case for yes, too

In 1905, Albert Einstein explained the photoelectric effect — light knocking electrons out of a metal — by proposing that light itself arrives in discrete packets of energy, later named photons. A photon's energy depends only on its frequency: E = h × f, where h is a tiny fixed number called the Planck constant. Dimmer light means fewer photons, not weaker ones; a very dim beam of high-frequency violet light can still knock an electron out, while an enormously bright beam of low-frequency red light, below the threshold frequency, cannot knock out a single one.

E = h × f
A photon's energy, where h ≈ 6.626 × 10⁻³⁴ joule-seconds (the Planck constant) and f is the light's frequency.
Green photon ≈ 2.25 eV
About 3.6 × 10⁻¹⁹ joules — a vanishingly small amount of energy for a single photon.
Red photon ≈ 1.77 eV, violet ≈ 3.10 eV
Higher frequency (shorter wavelength) always means more energetic photons.

Worked example

0 / 5 steps shown

How many photons is a laser pointer, really?

A small green laser pointer outputs about 1 watt of power (a strong one; most are far less). Using E = hc ÷ λ for one green photon (550 nm) and power = energy per second, roughly how many photons leave it every second?

Need a different angle?

Three centuries of arguing about what light is

  1. 1670s
    Newton: particles Proposed light is a stream of tiny particles ("corpuscles"), explaining reflection and straight-line travel well.
  2. 1670s
    Huygens: waves Proposed light is a wave in an invisible medium, explaining refraction (and, later, diffraction) at least as well.
  3. 1801
    Young: wave evidence The double-slit interference experiment gave strong, direct evidence for light's wave nature, and the particle theory fell out of favour for a century.
  4. 1860s
    Maxwell: electromagnetic waves Showed mathematically that light is an oscillating electric and magnetic field, unifying light, radio waves and all the rest of the electromagnetic spectrum.
  5. 1905
    Einstein: the photon Explained the photoelectric effect only by treating light as discrete energy packets, reviving the particle picture — and winning the 1921 Nobel Prize substantially for this, not for relativity.
  6. 1920s onward
    Quantum mechanics: both, properly A full theory (quantum electrodynamics) shows light is neither a simple wave nor a simple particle in the everyday sense, but a genuinely quantum object that shows either face depending on how you look at it.

Lab

Revisit dispersion and scattering, now knowing both are wavelength-dependent wave phenomena.

white light60° glass prismRedViolet
How far each colour is bent by the prism
ColourWavelengthGlass index nBent by
Red660 nm1.514238.54°
Orange610 nm1.515938.68°
Yellow580 nm1.517138.78°
Green540 nm1.51938.94°
Cyan500 nm1.521439.14°
Blue470 nm1.523639.33°
Violet425 nm1.527939.7°

Violet is bent 1.16° more than red. That is a small angle — but over a few metres it is enough to spread a whole rainbow across a wall. Long waves (red) are slowed least by the glass, so they bend least; short waves (violet) are slowed most, so they bend most.

Model: an equilateral crown-glass prism, index from the Cauchy formula n = A + B/λ². Reflections at the faces are ignored.

Round 1 / 6★ 0 ptsBest: 0

Predict before you peek: 6 quick questions about prism. Play with the lab above first if you like.

Text version of this activity

The same prism and scattering bench from earlier layers, worth one more look with the wave-particle debate in mind: dispersion (different wavelengths refracting by different amounts) and scattering (different wavelengths deflected by different amounts by small particles) are both explained through wavelength — a wave property. Nothing about the photoelectric effect or photon counting shows up here at all, which is itself an illustration of how differently the two faces of light present themselves.

Need a different angle?

Chapter 04

Lasers: light with one colour, one direction, one rhythm

Ordinary light, even from a single small bulb, is a chaotic mix: many different wavelengths, spreading in every direction, with every photon arriving out of step with every other. A laser (Light Amplification by Stimulated Emission of Radiation) produces something genuinely different: light of essentially one wavelength, travelling in one tightly focused direction, with all its waves rising and falling perfectly in step — a property called coherence.

Worked example

0 / 4 steps shown

A laser rangefinder, timing light instead of sound

A laser rangefinder fires a pulse at a wall 10.5 m away and times how long it takes to return. Light travels about 30.0 cm per nanosecond (a billionth of a second). How long does the round trip take, and why does this device need extremely fast electronics?

Need a different angle?
TableA few everyday and specialised uses of laser light
UseWhat the coherence or focus buys
Barcode and QR scannersA tightly focused, single-wavelength spot that reads a printed pattern reliably
Fibre-optic communicationA single, stable wavelength that stays sharp over many kilometres of glass fibre
Laser eye surgeryExtremely precise, focused energy delivered to a tiny, exact spot on the cornea
Laser rangefinders and LIDARA short, tightly focused pulse whose travel time gives distance to within centimetres
Laser pointers and light showsA narrow, undiverging beam visible as a sharp point or line from a distance

Lab

See a perfectly straight, undiverging beam — the geometric idealisation a laser approaches closely in practice.

Light ray reflecting from a flat mirrorThe incoming ray makes 0° with the normal; the reflected ray leaves at 0° on the other side of the normal.
Measured angles
Angle of incidence
Angle of reflection
Angle to the mirror surface90°

Ray model: a perfectly flat, smooth mirror. Real mirrors absorb a little light, and light also behaves as a wave.

Text version of this activity

A single ray travelling dead straight with no spreading, standing in for how closely a real laser beam approaches the idealised ray model used throughout this whole topic. An ordinary torch or bulb, by contrast, sends rays out from its source in every direction at once — a laser is the closest real-world object to "drawing a single ray" that physics actually offers.

Need a different angle?

Chapter 05

Project: measure the speed of light with a chocolate bar

Here is a real experiment you can try, using a microwave oven, a chocolate bar (or cheese, or marshmallows) and a ruler. It measures the speed of light using nothing more advanced than arithmetic — no lasers, no astronomy, no spinning wheels.

The chocolate-bar experiment, step by step

  1. Step 01Remove the turntablestep 1

    A microwave oven's turntable spreads the heating evenly, which hides the pattern this experiment needs. Take it out, with an adult's help, or prop the dish so it cannot spin.

  2. Step 02Lay chocolate flat on a microwave-safe dishstep 2

    A thin, even layer works best — break up a bar and lay the pieces edge to edge.

  3. Step 03Heat in short burstsstep 3

    Run the microwave for 10–20 seconds at a time, checking after each burst, until you see a few clearly melted spots rather than the whole bar melting evenly.

  4. Step 04Measure the gap between melted spotsstep 4

    The melted spots mark the hot points of the standing microwave pattern inside the oven, spaced by exactly half a wavelength.

  5. Step 05Find the oven's frequencystep 5

    Almost every microwave oven has its operating frequency printed on a label inside the door or on the back plate — typically 2.45 GHz (2.45 × 10⁹ hertz).

  6. Step 06Calculatestep 6

    Wavelength = 2 × (gap between melted spots). Speed = frequency × wavelength.

Worked example

0 / 4 steps shown

Working the chocolate-bar numbers

A student measures a gap of exactly 6 cm between two melted spots, and their oven's label reads 2.45 GHz. What speed do they calculate, and how close is it to the accepted value?

Need a different angle?

Chapter 06

A puzzle: the sunset that has already happened

Here is a genuine puzzle. The Earth's atmosphere is not uniform: it is denser near the ground and thinner higher up. Light travelling through a gradually changing density bends gradually too, curving very slightly downward as it approaches the ground — which means it curves the image of a distant object slightly upward as you see it.

Predict first

Because of this atmospheric bending, when you watch the Sun's lower edge appear to just touch the horizon at sunset, where is the Sun's true, geometric position?

Worked example

0 / 4 steps shown

How much extra daylight does bending give you?

Atmospheric refraction lifts objects near the horizon by about 34 arcminutes (34⁄60 = 0.567°). The Sun crosses the sky at about 360° in 24 hours. How many extra minutes of visible daylight does this bending add, roughly?

Need a different angle?

Lab

A simplified single-boundary model of the much more gradual bending that really happens across the whole atmosphere.

Light ray reflecting from a flat mirrorThe incoming ray makes 5° with the normal; the reflected ray leaves at 5° on the other side of the normal.normal
Measured angles
Angle of incidence
Angle of reflection
Angle to the mirror surface85°

Ray model: a perfectly flat, smooth mirror. Real mirrors absorb a little light, and light also behaves as a wave.

Text version of this activity

A ray box showing one sharp boundary bending a nearly horizontal ray slightly upward — a simplified stand-in for what really happens gradually, over many kilometres, as starlight or sunlight crosses air of continuously increasing density on its way down to the ground. Real atmospheric refraction has no single sharp boundary at all; it is a smooth curve, strongest exactly at the horizon where the path through the densest air is longest.

Need a different angle?

Chapter 07

Light-years and looking into the past

Because light takes real time to travel, every single thing you look at, you see slightly in the past — and the farther away it is, the further back in time you are looking. A light-year is simply the distance light travels in one year: about 9.46 trillion kilometres.

TableHow far into the past you are looking, for various objects
ObjectDistanceLight-travel time
The Moon384,400 km1.28 seconds
The Sun150 million km (1 AU)8 minutes 19 seconds
Jupiter (at opposition)about 4.2 AUabout 35 minutes
Proxima Centauri (nearest star)4.25 light-yearsabout 4 years 3 months
Sirius (brightest star in the night sky)8.6 light-yearsabout 8 years 7 months
The Andromeda Galaxy (naked-eye visible)2.5 million light-yearsabout 2.5 million years

Worked example

0 / 4 steps shown

Why you could never have a normal conversation with Proxima Centauri

Proxima Centauri, the nearest star beyond the Sun, is 4.2465 light-years away. If you sent a radio message there (radio waves travel at the same speed as light) and someone replied the instant they received it, how long would you wait for the reply?

Need a different angle?

Try it

years

Chapter 08

Open questions and where light takes people

Studying light seriously opens onto real careers and real unanswered questions — not just tidy textbook problems. First, two puzzles to try before you read the fields and questions below.

Worked example

0 / 3 steps shown

Puzzle: the satellite phone call delay

A television signal is bounced up to a geostationary satellite, 35,786 km overhead, and straight back down to a receiving dish. Using distance ÷ speed, how long does that one-way hop take, and why do satellite phone calls have such a noticeable pause?

Need a different angle?
TableA few fields built on understanding light
FieldWhat it uses
Optometry and ophthalmologyLens power, refractive errors, the eye's optics
Astronomy and astrophysicsTelescopes, spectra, look-back time, redshift
Fibre-optic and telecom engineeringTotal internal reflection, signal loss, latency
Photography and cinematographyLenses, exposure, colour, dynamic range
Remote sensing (ISRO and others)Satellites reading reflected and emitted light across many wavelengths, including infrared, to monitor crops, water and weather
Quantum information scienceIndividual photons used to carry and process information

Chapter 09

Pulling it together

Terms from this lesson

Electromagnetic spectrum
The full family of waves that includes radio, microwave, infrared, visible light, ultraviolet, X-rays and gamma rays, all travelling at the speed of light.
Diffraction
Waves spreading slightly around obstacles or through narrow gaps — evidence for light's wave nature.
Example: A CD's rainbow, or light spreading through a narrow slit.
Interference
Two overlapping waves reinforcing (brighter) or cancelling (darker) depending on their alignment.
Example: Young's double-slit banding pattern.
Photon
A discrete packet of light energy, with energy E = h × f.
Example: A green laser emits billions of billions of photons every second.
Photoelectric effect
Light knocking electrons out of a metal, only above a minimum frequency — evidence for light's particle nature.
Example: Explained by Einstein in 1905.
Wave–particle duality
The genuinely quantum fact that light (and matter) shows wave behaviour in some experiments and particle behaviour in others, with no contradiction.
Light-year
The distance light travels in one year, used to measure vast astronomical distances.
Example: Proxima Centauri is 4.25 light-years away.

Reflect

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Lab

Match six wave-and-particle terms to their meanings.

Match each extend-layer term to its meaning.

6 pairs are hiding in two mixed-up columns. Pick one from each side to join them.

Text version of this activity

A connect-the-pairs game covering this layer's core vocabulary: diffraction, interference, photon, the photoelectric effect, the light-year, and wave–particle duality.

Need a different angle?

Quick check

Test what you worked out

5 questions · answer what you can, then check. Getting one wrong is useful.

  1. Q1Compared with visible light, radio waves have:
  2. Q2Young's double-slit experiment provided strong evidence that light behaves as a:
  3. Q3A photon's energy is directly proportional to its:
  4. Q4Atmospheric refraction near the horizon:
  5. Q5A light-year measures:

Keep this

Cheat sheet

  • Electromagnetic spectrum: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma — all the same phenomenon, differing only in wavelength, all travelling at c.
  • Wave evidence: diffraction (bending round edges) and interference (Young's double slit, a CD's rainbow) — both need overlapping waves, not particles.
  • Particle evidence: the photoelectric effect and single-photon detection. E = h × f: a photon's energy depends only on frequency.
  • Wave–particle duality: light genuinely shows both behaviours; it is a quantum object, not secretly one or the other.
  • Atmospheric refraction lifts objects near the horizon by about 34 arcminutes, adding a couple of minutes of daylight at sunrise and sunset.
  • Light-year: the distance light travels in a year, about 9.46 trillion km. Looking far away always means looking into the past.

Related to

Electricity

Maxwell's 19th-century equations, which first showed light is an electromagnetic wave, are the very same equations behind how alternating current and generators work.

Used in

Anatomy of the human body

Detecting single photons in very low light is close to the physical limit of what the eye's retina can do — some experiments suggest a dark-adapted human eye can detect only a handful of photons.

Where this comes from

Sources

  • Introduction to the Electromagnetic Spectrum (opens another website) — NASA Scienceawaiting check

    Supports the ordering of the electromagnetic spectrum by wavelength from radio to gamma rays, and the idea that visible light is only a narrow slice of it.

  • Visible Light (opens another website) — NASA Scienceawaiting check

    Supports the visible spectrum's wavelength range (about 400 to 700 nanometres), the order of spectral colours, and visible light's place within the wider electromagnetic spectrum.

  • Light (opens another website) — Encyclopaedia Britannicaawaiting check

    Supports the general description of light as electromagnetic radiation, its dual wave and particle behaviour, and the historical development of ideas about what light is.

  • Speed of light (opens another website) — Wikipediaawaiting check

    Supports the historical timeline of measuring the speed of light, including Rømer's astronomical method and Fizeau's rotating toothed wheel experiment, and their results compared with the modern value.

  • The Rainbow (opens another website) — HyperPhysics, Georgia State Universityawaiting check

    Supports the geometry of the primary and secondary rainbow (refraction, one or two internal reflections, then refraction again in a raindrop), the primary bow's angle of about 42 degrees, and Alexander's dark band between the two bows.

End of Extend

What you just read

  • Place visible light within the wider electromagnetic spectrum by wavelength.
  • Give at least one piece of evidence each for light behaving as a wave and as a particle.
  • Carry out (or understand) a real measurement of the speed of light using a microwave oven.
  • Explain why atmospheric refraction adds a few minutes of daylight to every day.
  • Use light-years to say how far into the past you are looking at a given astronomical object.

The web

Explore a connection

  • Helps you understandanother area

    Eclipses

    An eclipse is a shadow, and shadows need light that travels in straight lines.

  • Helps you understandanother area

    Phases of the Moon

    The Moon has no light of its own: we see the half of it the Sun is lighting.

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Revision 1 · release preview-7e1cbbcc4f · accepted 20/09/2026