Light
Waves That Paint Reality
A Bright Spot in a Shadow
Light is a ripple in the electromagnetic field, but for a long time it seemed to be a stream of tiny particles, and the reason was shadows. Waves on a pond bend round a post, while light seems to run in straight lines and cast sharp shadows. Yet let sunlight into a dark room through a pinhole, hold a narrow slip of card in the beam, and its shadow shows bright and dark bands, where the light passing its two sides overlaps. Light added to light can make darkness, as only waves can.
A full wave theory of how light spreads round edges makes a prediction that sounds absurd. Behind a small round disc, it says, there is a bright spot at the very center of the shadow, where the shadow should be darkest. Stick a small metal disc to a glass plate and try it, and the spot is there.
The spot is there because every point of the disc’s rim is the same distance from the middle of the shadow, so the light that bends round the whole rim arrives there in step and adds up. Shadows can be sharp only because light’s waves are so short, a few ten-thousandths of a millimeter. Round anything that small, light spreads as freely as water round a post.
How Fast
For most of history it was not clear whether light took any time at all. The first sign came from Jupiter’s moon Io. While Earth was moving away from Jupiter, Io came out of Jupiter’s shadow a little later each time than its orbit predicted. One emergence was forecast to be ten minutes late, and it was. The delay was the light’s longer journey. The first estimate of that journey, about 22 minutes to cross Earth’s orbit, gave a speed about a quarter below today’s value.
Light can be timed on the ground, too. Send it between the teeth of a spinning wheel to a far mirror and back. Spun fast enough, the wheel moves a tooth into the returning light’s path, and the light is blocked. The first time this was done, with the mirror 8.6 kilometers away, the spin and the distance gave about 315,000 kilometers a second, five percent too high.
Why this speed? Picture a ripple of a given strength sweeping past a point: the faster it runs, the faster the field at that point changes. One of the field’s rules ties a changing magnetic field to the electric field around it, so the faster the ripple, the less magnetic field goes with a given electric field. The other ties a changing electric field to the magnetic field around it, so the faster the ripple, the more magnetic field goes with it. The two agree at one speed only, set by how hard charges push and currents pull, and that speed is light’s. Today it is exactly 299,792,458 meters a second by definition, and the meter is defined from it. Every observer measures that same speed in empty space, however fast they move, the fact relativity is built on.
Slower in Glass
In water light travels at three-quarters of its speed in empty space, and in glass at about two-thirds. Nothing in the glass holds it back. The light’s electric field shakes the electrons in every atom it passes, and each shaken electron sends out a little light of its own, a fraction of a swing behind. Added to the light that drove them, these wavelets make a wave whose crests advance more slowly. The light is not swallowed and sent out again atom by atom: the wavelets sent sideways cancel each other, and the beam stays a beam.
How much slower is a material’s refractive index, the speed in empty space divided by the speed of the crests inside: 1.33 for water, about 1.5 for glass, 2.42 for diamond. Almost everything else on this page follows from those shaken electrons.
Bending at the Boundary
Cross into glass at a slant, and the side of each crest that enters first slows first, so the whole front swings round, as a row of marchers turns when one end steps onto sand. The beam bends toward the line square to the glass’s face. An exact rule links the two angles to the two speeds.
Light from a straw in a glass of water turns as it leaves the water, which is why the straw looks broken at the surface. A lens is glass shaped so that each part of a beam turns by just the amount that brings them all to one point, and your eye has one that changes shape to focus. Even a flawless glass lens cannot make that point much smaller than half a wavelength, because light spreads round edges as the bright spot showed. That sets the finest detail an ordinary microscope can see.
Some light turns back at the face too. The shaken electrons in the glass also send part of it back. Their wavelets add up only in one direction, so it leaves at the angle it came in: about four percent from glass met square on, and more and more as it comes in closer to skimming the face. Coming out of glass into air, light speeds up and turns away from the line square to the face. Striking the face from inside at more than about 42 degrees from that line, it would have to turn beyond the face itself, so none gets out and all of it reflects back. Glass fibers that carry the internet trap light the same way, at the boundary between the core and a coat of glass that slows light slightly less.
Timed directly, light is indeed slower in water than in air. In the old particle picture, light would have had to speed up in water to bend the way it does, so that measurement ended the picture. Light was later found to arrive in whole lumps, but each lump is a ripple of the field, traveling as a wave, not a little bullet.
Colors Part
Glass slows violet light a little more than red. Its electrons respond most strongly to ultraviolet, and the nearer light’s frequency comes to theirs, the harder they answer and the more they slow it. So each color bends by its own amount. Let sunlight through a hole in a shutter into a glass prism, and it spreads into a band of colors on the far wall. In the classic version of this test, the band was about five times longer than it was wide. A single color passed through a second prism does not split again. The colors are in the white light from the start, and the prism only sorts them.
A raindrop does the same, with one reflection inside. Sunlight enters a drop all over its face and comes back out at many angles, but never more than about 42 degrees from the point opposite the Sun for red, or 40 for violet, and near that limit the rays pile up. So a rainbow is a circle round the point opposite the Sun, red on the outside, and each drop at the right angle sends you one color. Inside the bow, drops send back light of every color, and the sky there is brighter. Light reflected twice inside a drop makes a fainter second bow, colors reversed, at about 51 degrees. Between the two bows the drops send you almost nothing, and the sky is darker there, a stripe known as Alexander’s band.
Why the Sky Is Blue
The same shaken electrons send some light sideways. In glass the atoms are packed so tightly that every small patch holds almost the same number, and their sideways wavelets almost cancel. What little they scatter is what dims light in a long glass fiber. In air the molecules are a few millionths of a millimeter apart, far closer than a wavelength, but they are sparse and wander freely, so the count in each small patch keeps changing. The cancelling is far from complete, and each scatters as if alone. Things that small next to the wavelength favor short waves steeply: the scattering grows as the fourth power of the frequency, so blue light at 450 nanometers scatters almost six times as much as red at 700. Look anywhere away from the Sun and you see sunlight scattered toward you, mostly blue. The sky is not violet, though violet scatters more still, because sunlight holds less of it and our eyes are less sensitive to it.
At sunset the Sun’s light reaches you through far more air. Most of its blue has been scattered out on the way, and what is left is orange and red. A beam sent through a cloud of very fine particles in a glass tube looks blue from the side. A few drops of skim milk in a tank of water do much the same: its specks of protein are several times smaller than light’s waves. Mars shows what coarser specks do. Its dust grains are a few thousandths of a millimeter across, larger than light’s waves. They absorb blue, which turns the daytime sky butterscotch, and they throw blue light forward, close round the Sun, so the sky round the setting Sun is blue.
Which Way It Swings
Light’s electric field swings across its direction of travel, and the swing has a direction. In sunlight or lamplight it changes at random from instant to instant. A polarizing filter is a sheet of long molecules lined up one way. Electrons run easily along them, so a swing along the molecules drives currents that soak up its energy, while a swing across them passes. A line marked on each filter shows the direction it passes. Turn a second filter behind the first and the light dims. Crossed at a right angle, the two pass almost nothing.
Light scattered by the sky at right angles to the Sun is strongly polarized, and so is glare off water or a wet road, which swings mostly level. Polarized sunglasses pass only the upright swing and cut the glare. Bees see the sky’s polarization and steer by it when the Sun is hidden. And most liquid-crystal display (LCD) screens are a sandwich of two crossed filters with a liquid crystal between them that changes the swing, pixel by pixel, to let light through.
Light at a Car’s Pace
Atoms can hold back a pulse of light far more than glass slows its crests. In a cloud of sodium atoms cooled to fifty billionths of a degree above absolute zero, a pulse of light has been slowed to 17 meters a second. A second laser makes the cloud clear in a narrow band of colors, and in that band the pulse drags a swing of the atoms along with it. A pulse can even be stored and sent on later, in such a cold cloud and also in warm rubidium vapor at about 80 degrees Celsius, so storing light needs no extreme cold. Switching off the second laser hands the light’s pattern to the atoms, and switching it back on sends it out again as light. What stands still is not the light, but the pattern it carries.
