What Light Is

Strike a match in a dark room and the room appears. The walls, the chair, your own hand: none of them were missing a moment ago. Something left the flame, crossed the room faster than you could notice, bounced off everything in it, and some of it reached your eyes. This page is about that something: what it is, how fast it goes, what happens when it meets glass and water and other light, and how your eye turns it into color.

We'll start with the plainest facts about light, the ones you can check with a lamp and a box. Drag the lamp around the room, and widen it from a pinpoint to a frosted bulb across. Watch the shadow the box throws on the wall:

Three facts are in that figure. Light leaves the lamp in straight lines: a shadow is the region of the wall that no straight line from the lamp can reach. A wide lamp gives the shadow a dark core, the umbra, which no part of the lamp can see, and gray edges, the penumbra, which see some of it. Shrink the lamp to a point and the edges go sharp.

The third fact is in the readout. Pull the lamp back from the wall and the wall dims, and not in proportion: twice as far, a quarter as bright. The light leaving the lamp spreads over a sphere whose area grows with the square of its radius, so the same light is shared over four times the area. That's the inverse-square law, and it's why a candle across a hall barely lights the far wall.

How fast#

Light seems to arrive the instant the match is struck. Galileo tried to time it around 1638 with two lanterns on hilltops a mile apart, uncovering one when he saw the other, and found no delay he could measure.1His reaction time was a few tenths of a second. Light crosses a mile in about five millionths of one. To measure something that fast you need either a very long baseline or a very fast clock. The first measurement used the longest baseline available: the orbit of the Earth.

In the 1670s the Danish astronomer Ole Rømer was timing the eclipses of Io, the innermost large moon of Jupiter, which disappears into Jupiter's shadow every 42.5 hours. The eclipses should tick like a clock. They didn't: some months they came early, some months late. Drag the Earth around its orbit and watch when we see Io vanish:

When Earth is on the far side of its orbit from Jupiter, every eclipse arrives about 16 and a half minutes later than when Earth is closest. Nothing changed at Jupiter. The light announcing each eclipse simply had farther to travel: the extra distance is the width of Earth's orbit, about 300 million kilometers. Rømer predicted in 1676 that an eclipse due in November would be seen ten minutes late, and it was [1].

Rømer's own estimate was 22 minutes for the orbit's width, and his contemporaries didn't know that width well either. Christiaan Huygens combined the two into a speed of about 220,000 km/s. It was wrong by a quarter, but it was the first time anyone had shown that light takes time at all.

The next step needed a clock fast enough to time light across a few kilometers. In 1849 Hippolyte Fizeau built one from a spinning wheel with 720 teeth [2]. Light passes through a gap between two teeth, travels 8.6 km to a mirror on a distant hill, and comes back through the wheel. Spin the wheel up to and watch whether the returning light gets through:

At rest, light goes out through a gap and comes back through the same gap. Spin the wheel and the returning light finds the gap a little further along; at 12.1 turns a second the wheel turns exactly half a tooth spacing in the 58 microseconds the light is away, a tooth sits where the gap was, and the light goes dark. Spin twice as fast and the next gap arrives in time, so the light comes back.

Fizeau saw the first dark at 12.6 turns a second. From that, the speed of light is four times the distance, times the number of teeth, times the spin rate: about 313,000 km/s, within 5% of the modern value. Today the number is no longer measured at all. Since 1983 the meter is defined as the distance light travels in 1/299,792,458 of a second, so the speed of light is exactly 299,792,458 m/s [3].

A wave of fields#

Fast, straight, spreading: none of that yet says what light is. The answer came from an unexpected direction. In the 1860s James Clerk Maxwell wrote down the laws of electricity and magnetism in four equations, and noticed that they allow a disturbance to travel on its own: a changing electric field makes a magnetic field, which, changing, makes an electric field again, and the pair leapfrogs through empty space. He worked out its speed from two constants measured in laboratory experiments with charges and currents. It came out at 310,000 km/s, the speed of light [4].

Here is a stretch of that wave, frozen in time and then let go. The electric field pushes up and down, the magnetic field side to side, both crosswise to the direction of travel. Turn it to see the two fields from the side and from above:

The two fields rise and fall together and point at right angles to each other and to the direction of travel; light is a transverse wave, like a wave on a rope rather than a sound wave in air. The distance from one crest to the next is the wavelength. In visible light it's tiny: between 380 and 750 billionths of a meter, about a hundredth of the width of a hair.

A wave moving at a fixed speed that's this short must shake very fast. The number of crests passing a point each second, the frequency, is the speed divided by the wavelength. Slide the wavelength across the visible range and watch the color and the frequency:

Every color in the rainbow is just a wavelength: about 450 nm looks blue, 530 green, 570 yellow, 650 red. The frequencies are absurd. Green light at 532 nm shakes 564 trillion times a second, which is why no camera, no wire, no electronic circuit can follow the field of a light wave directly; we only ever measure how much energy it delivers.

Nothing special happens at the ends of the slider. The same kind of wave exists at every wavelength; our eyes just stop responding below about 380 nm and above about 750. Drag along the whole family, from radio to gamma rays, on a scale where each step is ten times the last:

Radio, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays are all the same thing: electric and magnetic fields leapfrogging at 299,792 km/s. They differ only in wavelength, which spans about 25 powers of ten, from the size of an atomic nucleus to the size of a city. What changes along the way is how the wave interacts with matter. Radio waves pass through walls, visible light doesn't, X-rays pass through flesh but not bone. The status line also gives each wave's photon energy, a number that won't make sense until much later on this page, where it turns out to matter more than anything else.

Bouncing#

Light that hits something does one of three things: it bounces off, it goes in and gets absorbed, or it goes through. Start with bouncing. Drag the lamp and the eye above a flat mirror and watch which ray connects them:

However you place them, the ray that connects lamp and eye leaves the mirror at the same angle it arrived, measured from the normal, the dashed line standing straight up from the surface. That is the whole law of reflection. It has a striking consequence: trace the reflected rays backward and they all meet at one point behind the mirror, the image, as far behind the glass as the lamp is in front. Your eye can't tell those rays didn't start there, which is why a mirror looks like a window into a second room.

Most things aren't mirrors, though. Paper reflects nearly as much light as aluminum foil, yet you can't see your face in it. The difference is in the surface at the scale of the wavelength. Roughen a mirror, from polished to , and send a parallel beam at it:

A rough surface is a jumble of tiny mirrors facing every way. Each ray still obeys the law of reflection at its own little facet, but the facets disagree, so the light leaves in all directions. That's diffuse reflection, and it's how you see almost everything: light from a lamp lands on the page and leaves toward every eye in the room. A polished surface keeps the rays in order, which is why it shows you an image and paper shows you only itself.

Bending#

Now the light that goes in. Put a straw in a glass of water and it looks broken at the surface. Light crossing from air into water changes direction. Tilt the ray to from the normal and compare water, glass, and diamond:

Going in, the ray bends toward the normal: the angle inside, ${\theta }_2$, is always smaller than the angle in air, ${\theta }_1$, except straight on, where nothing bends. Diamond bends it most, water least. The rule was measured by Willebrord Snell in 1621 and is named after him:

Each material has a number $n$, its refractive index: 1.000 for air, 1.333 for water, about 1.52 for window glass, 2.42 for diamond. The status line also shows the share that bounces off instead, about 2% for water at this angle, rising toward 100% as the ray grazes the surface. That's why a lake mirrors the far shore but you can see straight down into it at your feet.

Why should light bend at all? The index has a second meaning: it's how many times slower light travels in the material. In water light does 225,000 km/s, in diamond 124,000. Think of a beam not as a line but as a row of crests marching side by side, like a marching band crossing from pavement onto mud at a slant. Send a beam into the glass at and watch its crests:

The side of each crest that touches the glass first slows down first, while the rest is still going full speed in air, so the crest swings round. Once the whole crest is inside, it marches on in its new direction. The crests also bunch up: the light shakes at the same rate inside the glass, but covers less distance per shake, so its wavelength there is shorter by the same factor $n$. Snell's law is just the geometry of that turn, worked out in the box below.

Bending has an everyday trick to it. Stand at the edge of a pool and look at a coin on the bottom. Drag the eye round from overhead to , looking across the water more and more, and watch where the coin seems to be:

Leaving the water, light bends away from the normal, and your brain traces it back in a straight line to a point higher than the coin. Straight overhead a pool looks three quarters as deep as it is, 1.5 m for a 2 m pool, because the index of water is 1.33. Look from straight overhead, then from a low slant, and the coin rises toward the surface. Anyone who has stepped into a pool expecting it to be shallower has met Snell's law; spear fishers learn to aim low.

Trapped light#

Run the bending backward and something new happens. Light leaving glass for air bends away from the normal, so the angle in air is always bigger than the angle in glass. At some angle inside, the angle outside reaches 90°: the ray skims along the surface. Beyond that, there's no angle left for it to take. Inside a half-disc of glass, aim a ray at the flat face at , and watch the share that reflects:

Below the critical angle most of the light gets out, a little more reflecting each degree. Then, at 41.2° for glass, the outgoing ray lies flat along the surface, and one degree past it there is no outgoing ray: 100% of the light reflects. This is total internal reflection, and it's a better mirror than any metal, which always absorbs a few percent. Diamond's critical angle is only 24.4°, so light that gets into a cut diamond bounces around inside many times before it finds a way out, which is much of its sparkle.

Make the glass long and thin and light can be carried around corners. Send a fan of light into one end of a bent rod of clear acrylic, and tighten the bend to :

Every time a ray meets the wall at more than 42° from the normal, all of it reflects, and the light zigzags along the rod and out of the far end. A gentle bend loses nothing. Bend it too tight and rays hit the outer wall too steeply and escape; you can see the same glow where an optical fiber is kinked. Telephone and internet traffic travels this way, through glass fibers a tenth of a millimeter thick with a core of slightly higher index than its sheath, so pure that light crosses 20 km of it and loses only half its strength [5].

Colors from white#

The refractive index isn't quite one number. In glass, violet light travels a little slower than red, so it bends a little more. Isaac Newton let a beam of sunlight through a hole in his shutter in 1666 and put a prism in its path. Do the same: aim a narrow beam of white light at the prism and compare window glass with lead glass:

White light isn't a color of its own. It's every visible wavelength at once, and a prism sorts them by how much each one slows down in the glass. That spread is called dispersion. In lead glass the index falls from 1.647 for violet to 1.615 for red, a difference of only 2%, but it's enough to fan the colors a few degrees apart. Newton's real insight was the next step: he picked out one color with a second hole and sent it through a second prism, and it stayed one color. The prism doesn't add color to white light; it separates what was already there.

A rainbow is the same separation, done by billions of raindrops at once. Start with one drop. Sunlight arrives as a parallel beam; follow one ray that enters the drop of the way from its center to its edge, bounces once off the back, and comes out:

Slide the entry point from the center to the edge and the exit angle climbs, levels off at about 42°, and comes back down. Rays near the turn all leave at nearly the same angle, so light from a whole band of the drop piles up there, while other angles get only a thin share. That pile-up is the rainbow. And because red's peak sits at 42.3° and violet's at 40.6°, the colors pile up at slightly different angles [6].

Now step back from the drop. Every drop in the sky sends its piled-up light out at 42° from the direction the sunlight is going. You only see the drops sitting exactly 42° from the point directly opposite the sun, which is the shadow of your own head. Those drops form a circle around it. Raise the sun to above the horizon:

The bow is a circle centered on the shadow of your head, and the ground cuts it off. At sunset the center sits on the horizon and you get a full half-circle. As the sun climbs the circle sinks, and with the sun more than 42° up there's no rainbow at all: rainbows belong to mornings and late afternoons. Light that reflects twice inside each drop makes a fainter second bow at 51° with the colors flipped, and the sky between the two bows is darker than anywhere else: no drop there sends you light that reflected once or twice.

Focusing#

Curve a piece of glass and refraction stops being a nuisance and becomes a tool. A lens is thicker in the middle than at the edges, so a ray hitting it far from the center meets a more steeply tilted surface and bends more. Done right, every ray from one point of an object bends just enough to meet again at one point behind the lens. Drag the candle toward the lens, or change the lens's focal length to :

Far from the lens, the candle's image forms just beyond the focal point F, small and upside down: that's how the lens in your eye and in a camera puts a picture on the retina or the sensor. Bring the candle closer and the image moves back and grows; at twice the focal length it's life size. Bring it inside the focal length and the rays leave the lens still spreading, never to meet. Your eye traces them back to a larger, upright image on the same side: a magnifying glass. All of it follows from one formula, $1/d_o+1/d_i=1/f$.

The ray picture hides what a lens does to the wave. Watch the crests leaving a point of light: they spread as circles, and the lens, slowing the middle of each crest more than its edges because the glass is thicker there, turns them inside out. Move the lens to from the light:

Out of the light come circles; out of the lens come circles curving the other way, each one shrinking as it goes until it closes to a point at the image, then spreading again beyond it. A focus is where the crests from every part of the lens arrive in step. Keep that picture of crests arriving together or not, because the next thing light does can't be explained any other way.

Light meets light#

In 1801 Thomas Young, a physician who later helped decipher the Rosetta Stone, made the case that light is a wave with a question about water. Two stones dropped into a pond send out two sets of ripples. Where the ripples overlap, what does the water do? Run two steady sources side by side, apart, and watch the water between them:

Where a crest from one source meets a crest from the other, the water heaves twice as high. Where a crest meets a trough they cancel, and along certain calm lines the water barely moves. Those lines run wherever one source is half a wavelength farther away than the other, or one and a half, or two and a half. Move the sources farther apart and the lines multiply and crowd together. The shore at the bottom shows the result: bands that get pounded, and bands between them that stay still. This adding and cancelling is called interference, and only waves do it. Two streams of pellets would simply add up.

Young showed that light does the same [7]. In the version taught today, one color of light shines through two narrow slits a fraction of a millimeter apart, and each slit becomes a new source of ripples. On a screen a meter behind them, the two add or cancel. Set the light's wavelength to and the slits apart, then drag the marker along the screen:

The screen fills with stripes. At the center both slits are the same distance away, so their light arrives in step and adds. A little off center the far slit's path is half a wavelength longer and the light cancels; a whole wavelength longer, it adds again. The stripes sit $\lambda L/d$ apart, where L is the meter to the screen and d the gap: 2.1 mm for green light through slits a quarter millimeter apart. So a ruler measures the wavelength. Young, working from Newton's measurements of colored rings, put the ends of the spectrum at about 675 nm for the deepest red and 425 nm for violet [8].

No stream of pellets gets brighter anywhere when you block half of it. With one slit open the screen shows one broad patch; the dashed line marks the old stripes.

You don't need slits to see interference. A soap film does it with two reflections. Some light bounces off its front surface, and some goes in and bounces off the back, traveling an extra two thicknesses of film. Where that detour puts the two reflections in step for a color, the film shines in that color; colors whose reflections cancel are missing from what you see. A soap film in a wire loop drains as it stands, so it's thinnest at the top. Set its thickness to :

The whole film is a few hundred nanometers thick, a hundredth of a hair, and its colors are a map of that thickness. Near the top, thinner than about 30 nm, the two reflections cancel at every wavelength, because the reflection off the front flips the wave over and the one off the back doesn't. The film turns black there, shortly before it pops. Lower down come yellow, magenta, and blue, then greens and pinks, fading toward white where the film is thick. Oil on a wet road and the purple sheen of a coated camera lens are the same effect [9].

Sideways waves#

A wave on a rope can shake up and down or side to side. The direction a light wave's electric field shakes in is its polarization, and light from a lamp or the sun is a jumble of every direction at once. A polarizing filter is a plastic sheet of long molecules all lined up, which soak up the part of the field that shakes along them and pass the part that shakes across them. Send lamp light through one filter, then through a second turned from the first:

The first filter passes half the lamp's light, whatever way it's turned: of a jumble of directions, on average half the field lies along it. The second filter passes the share ${\cos }^2\theta$ of what reaches it, a rule Étienne-Louis Malus found in 1809 [9]. Lined up, the second filter hardly matters; crossed at 90°, it blocks everything. In between, it keeps only the part of the field that lies along its own lines, so the light comes out weaker and shaking in a new direction. The plot in the corner is that rule.

Light also gets polarized by bouncing. When sunlight reflects off water, the part of the field that shakes parallel to the surface reflects far more readily than the part that shakes up and down. Move the sun to from overhead and compare the sideways and the up-and-down shaking light in the reflection:

At one angle, 53° for water, the up-and-down part doesn't reflect at all. This is Brewster's angle, where the tangent of the angle equals the refractive index, found by David Brewster in 1815 [10]. Near it, the glare off a lake or a wet road is almost all sideways-shaking light. Polarized sunglasses use that: their filters pass only up-and-down shaking light. Put them on and the glare at 53° disappears, while light from everything else, which isn't polarized, gets through at half strength. Anglers wear them to see past the reflection into the water.

The sky is polarized too, and for the same reason it's blue. Sunlight crossing the air sets the electrons in each nitrogen and oxygen molecule shaking, and each shaking molecule sends out light of its own in other directions: it scatters it. Molecules far smaller than a wavelength scatter in proportion to $1/{\lambda }^4$, so violet light is scattered about nine times as strongly as red [11]. Lower the sun to above the horizon:

Look anywhere away from the sun and what reaches you is scattered light, mostly blue: that's the sky. Look at the sun itself and you see what's left. Near the horizon its light crosses nearly forty times as much air as from overhead [12], the blue is scattered away, and the sun goes yellow, orange, and red. The sky isn't violet, though violet scatters most, because sunlight carries less violet and our eyes are less sensitive to it. And a shaking molecule sends no light along the line it shakes in, so skylight 90° from the sun is strongly polarized: look there through polarized sunglasses and tilt your head, and the sky darkens.

Lumps of light#

By 1900 the wave picture explained everything above, and one experiment refused to fit. Light shining on a clean metal can knock electrons out of its surface, the photoelectric effect. If light were only a wave, brighter light would shake the electrons harder and fling them out faster, and any color would do if it were bright enough. Before you try it, make a prediction:

Pick a color and a metal, and turn up the brightness. The wavelength is now :

Below a certain frequency nothing comes out, however bright the light. Above it electrons leave at once, even in dim light, and brighter light frees more of them but no faster ones. Only the color sets their top energy. Einstein's explanation, in 1905, was that light delivers its energy in lumps, now called photons, each carrying energy $E=hf$, where h is Planck's constant [13]. One photon frees one electron, which pays a fixed toll to get out, the metal's work function [14], and leaves with the rest. Plot the top electron energy against frequency and every metal gives a straight line with the same slope, h. Robert Millikan, who doubted Einstein's idea, spent years on the measurement and in 1916 found exactly that line [15].

So is light a wave or a stream of lumps? The answer shows up in one experiment. Dim the light in Young's two slits until photons pass through one at a time. Each one lands at a single spot, like a particle. Send them through at and watch the spots pile up:

The first few dozen spots look scattered at random. After a few thousand, the stripes appear: photons almost never land where the waves from the two slits would cancel. G. I. Taylor did a version of this in 1909 with light so feeble that his longest exposure took about three months, and the fringes came out as sharp as in bright light [16]. The wave tells you where a photon is likely to land, and its prediction matches the tally; the photon itself arrives whole, in one place. Electrons sent through two slits stripe a screen the same way.

Three numbers#

The last stop is the eye. Its lens focuses an image on the retina, where about six million cone cells catch photons in daylight. They come in three kinds, called short, medium, and long after the wavelengths they respond to best, near 440, 540, and 570 nm [17]. A cone that absorbs a photon can't tell what color it was: a photon either triggers it or doesn't, and all the cone reports is how often. Its sensitivity curve only sets the odds. Shine light of one wavelength, , on all three:

Each wavelength gets its own mix of three numbers. At 450 nm the short cones fire hard and the others hardly at all: blue. At 570 nm the short cones are silent, the long ones at their peak, and the medium ones about four-fifths as strong: yellow. On its own, the long cone answers the same to a dim light at its peak and a bright one at 620 nm, so it can't tell color from brightness. Only the comparison between kinds of cone carries color, which is why people born with two kinds instead of three confuse colors that others tell apart easily.

Your brain never sees the spectrum, only those three numbers. So two lights with completely different spectra look identical if they produce the same three numbers. On the left is pure yellow light at 570 nm. On the right, mix a red light at 640 nm with a green one at 540 nm, and try to make the bars match:

With about 1.13 parts red to 0.71 parts green, the bars line up: every kind of cone responds to the mixture exactly as it does to pure yellow, and the two patches look the same, though one contains no yellow light at all. Lights that differ in spectrum but look identical are called metamers, and every screen depends on them. A phone shows yellow by lighting red and green subpixels side by side, and white by lighting all three. It never reproduces the spectrum, and it doesn't need to, because your eye never measures it.

Look back at the candle you started with. Its flame sends out every visible wavelength at 300,000 kilometers a second, a wave of fields shaking hundreds of trillions of times a second. Some of that light bends through the lens of your eye to a focus on the retina, and there it stops being a wave: each photon is caught whole by a single cone. Three kinds of tally reach the brain, and the brain turns three numbers into the warm yellow of a flame. Everything on the way, from the speed to the rainbow to the stripes behind two slits, comes from light being a wave. The counting at the end comes from its arriving in lumps.

References#

1. O. Rømer, “Démonstration touchant le mouvement de la lumière trouvé par M. Römer de l'Académie Royale des Sciences”, Journal des Sçavans (7 December 1676), 233–236.
2. H. Fizeau, “Sur une expérience relative à la vitesse de propagation de la lumière”, Comptes Rendus de l'Académie des Sciences 29 (1849), 90–92.
3. Bureau International des Poids et Mesures, The International System of Units (SI), 9th edition (2019).
4. J. C. Maxwell, “A dynamical theory of the electromagnetic field”, Philosophical Transactions of the Royal Society of London 155 (1865), 459–512.
5. K. C. Kao and G. A. Hockham, “Dielectric-fibre surface waveguides for optical frequencies”, Proceedings of the IEE 113 (1966), 1151–1158.
6. H. M. Nussenzveig, “The theory of the rainbow”, Scientific American 236:4 (1977), 116–127.
7. T. Young, “Experiments and calculations relative to physical optics” (Bakerian Lecture), Philosophical Transactions of the Royal Society of London 94 (1804), 1–16.
8. T. Young, “On the theory of light and colours” (Bakerian Lecture), Philosophical Transactions of the Royal Society of London 92 (1802), 12–48.
9. E. Hecht, Optics, 5th edition, Pearson (2017).
10. D. Brewster, “On the laws which regulate the polarisation of light by reflexion from transparent bodies”, Philosophical Transactions of the Royal Society of London 105 (1815), 125–159.
11. J. W. Strutt (Lord Rayleigh), “On the light from the sky, its polarization and colour”, Philosophical Magazine 41 (1871), 107–120 and 274–279.
12. F. Kasten and A. T. Young, “Revised optical air mass tables and approximation formula”, Applied Optics 28 (1989), 4735–4738.
13. A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt”, Annalen der Physik 17 (1905), 132–148.
14. H. B. Michaelson, “The work function of the elements and its periodicity”, Journal of Applied Physics 48 (1977), 4729–4733.
15. R. A. Millikan, “A direct photoelectric determination of Planck's ‘h’”, Physical Review 7 (1916), 355–388.
16. G. I. Taylor, “Interference fringes with feeble light”, Proceedings of the Cambridge Philosophical Society 15 (1909), 114–115.
17. A. Stockman and L. T. Sharpe, “The spectral sensitivities of the middle- and long-wavelength-sensitive cones derived from measurements in observers of known genotype”, Vision Research 40 (2000), 1711–1737.