Light

Light seems to arrive the instant a lamp is switched on. In fact it takes time, though very little. In empty space light covers about 300000 kilometres every second, fast enough to circle the Earth seven and a half times in that second. Nothing that carries matter or a message has ever been found to go faster.

Across the gulfs of space, even that speed means long delays. Sunlight needs about eight minutes to reach us. For the stars, astronomers use a larger measure, the light year: the distance light covers in one year, about nine and a half trillion kilometres. A star 100 light years away is seen by light that left it 100 years ago. So to look far out into space is to look back in time. A telescope shows each star as it was when its light set out, not as it is tonight.

How does an eye see a tree? For many centuries the leading mathematical answer, taught by Euclid and Ptolemy, was that the eye sends out rays that touch whatever it looks at. Around 1030, in Cairo, the scholar Ibn al-Haytham argued in his Book of Optics that the traffic runs the other way. Stare at the Sun and it hurts. Look away and a glowing spot lingers. Both show light acting on the eye. So sight, he concluded, begins when light enters the eye.

In outline, his account is the one we still use. Light leaves a source such as the Sun or a lamp. It strikes an object, which throws it back in all directions. A little of it enters your eye, and you see the object. That is why things that give out no light, like a tree or this page, can be seen: light bounces off them.

Ibn al-Haytham did not rest his optics on argument alone. He set several lamps at different places outside a darkened room that had one small opening. Inside, each lamp made its own spot of light on the facing wall. When he covered one lamp, only the spot opposite it vanished. Each beam had crossed the opening in a straight line, without mixing with the others. Settling a question by a planned test of this kind is an experiment, and he made it the test of claims about light.

A dark room with a small hole is known by its Latin name, camera obscura. Light from a whole scene outside passes through the hole and paints a picture of it on the wall. Because the rays travel straight and cross at the hole, light from the top of the scene lands at the bottom. The picture is upside down.

What happens when light meets a surface it cannot pass through? Some of it bounces off. This is reflection, and on a smooth, shiny surface it obeys one simple law: a ray leaves at the same angle as it arrived. The two angles are equal, like those of a ball bouncing off a wall. A mirror is smooth enough to keep the rays in order, so they still carry a picture.

That explains a mirror’s oddest trick. Light from your face bounces off the glass into your eyes, and your brain assumes it came in a straight line. So you see a face that seems to stand behind the mirror, where no light ever goes. An image like that, which light only appears to come from, is called a virtual image. The Moon, a rougher reflector, makes no light of its own and shines only with light from the Sun.

A straw standing in a glass of water looks broken at the surface. The straw is fine. The light coming from its lower half has changed direction on its way out of the water. This bending of light where it crosses from one clear material into another is refraction.

The cause is a change of speed. Light is fastest in empty space, and air barely slows it. In water it drops to about 225000 kilometres a second, and in glass to about 200000. Picture a line of marchers walking at an angle from a pavement onto mud. Each marcher slows on reaching the mud, the near end of the line before the far end, and so the whole line swings round to a new heading. A beam of light that slows as it enters glass at an angle turns in the same way, and turns back as it leaves.

If glass bends light, can it be shaped to bend light usefully? A lens is a piece of glass or clear plastic with curved faces. One that bulges outward in the middle, thick at the centre and thin at the edge, is a convex lens. Rays striking it are bent inward, each by a different amount, so that parallel rays all meet at a single point beyond it, called the focus.

Hold a convex lens in sunshine and you can find that point. The lens gathers all the sunlight falling on its face into one bright dot, hot enough to scorch paper. Hold the same lens close to a page and it works as a magnifying glass, making the print look larger. Cameras, microscopes and spectacles are all built from lenses doing these two jobs.

Your eye is a small dark room of its own. Light enters through the pupil, the hole at the front. The curved, clear front surface of the eye does most of the bending, and a flexible convex lens just behind the pupil does the rest, bringing the rays to a focus. The picture forms on the retina, a layer of light-sensitive cells lining the back of the eyeball. As in any camera obscura it lands upside down, and the brain makes sense of it.

For the picture to be sharp, the focus has to fall exactly on the retina. In many eyes it falls a little in front, which blurs distant things, or a little behind, which blurs near ones. Spectacles solve the problem with one more lens. Placed in front of the eye, it bends the rays slightly before they enter and moves the focus onto the retina.

Where do colours come from? In the 1660s most scholars held that white light was pure and simple, and that glass or water somehow stained it. Isaac Newton tested the idea in a darkened room in 1666. He let a thin beam of sunlight pass through a triangular glass prism. Out came not a white spot but a band of colours on the wall, running from red through orange, yellow, green and blue to violet. He called the band a spectrum.

Then came the decisive step. He let just one colour from the band pass through a second prism. It bent again but stayed the same colour, so the glass was adding nothing. Newton’s conclusion, published in 1672, was that white light is all colours mixed together. A prism only sorts them, because it bends each colour by a different amount.

A rainbow is a spectrum hung in the sky, and it needs two things at once: the Sun behind you and rain in front. The prisms are the raindrops. Soon after 1300 two scholars who never heard of each other, Kamāl al-Dīn al-Fārisī in Persia and the German friar Theodoric of Freiberg, worked out how. Al-Fārisī, who was revising Ibn al-Haytham’s Book of Optics, reasoned that a drop is too small to study, so he made a big one: a glass sphere filled with water, set in a dark room with a beam of sunlight falling on it.

Following the beam, he found that it bends as it enters the sphere, reflects off the inside of the far wall, and bends again as it leaves. The two bendings spread the colours apart. Millions of drops, each sending one colour toward your eye, paint the bow.

What makes red light red? Light travels as a wave, and each colour has its own wavelength, the distance from one crest of the wave to the next. These lengths are tiny. Red, the longest we can see, is about 700 nanometres, or billionths of a metre. Green is about 550 and blue about 450.

Wavelength decides how light fares in air. The molecules of the air scatter short waves far more strongly than long ones, knocking them off course in every direction. Blue is scattered about six times as much as red. So on a clear day blue light reaches your eye from all over the sky, while the other colours mostly travel straight on. At sunset the Sun’s light crosses far more air on its slanting path. Most of the blue is scattered away before it arrives, and what is left is red.

Is there anything beyond the two ends of the spectrum? In 1800 the astronomer William Herschel held a thermometer in each colour of a prism’s spectrum in turn, and the readings rose from violet to red. Then he tried just past the red end, where nothing could be seen. There it warmed the most. Invisible rays were falling there, with waves longer than red. They are now called infrared, the warmth you feel from a fire. A year later rays were found beyond the violet end too, with shorter waves: ultraviolet, the part of sunlight that burns skin.

Both are light in every way except that our eyes do not respond to them. The full family is called the electromagnetic spectrum. Running from the longest waves to the shortest, it holds radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. The colours we see are one narrow band.

Walk away from a street lamp and your book quickly becomes too dim to read. The lamp is giving out exactly as much light as before. What changes is how thinly that light is spread. Light leaves a lamp in all directions, like the skin of a swelling balloon. At twice the distance, the same light has to cover a surface four times as large, so each patch of your page receives a quarter as much: 25 per cent. At three times the distance it is spread over nine times the area and is down to a ninth.

This is the inverse-square law: brightness falls off with the square of the distance. It is why a reading lamp works best close to the page, and why the Sun, 150 million kilometres off, is blinding, while stars that are just as powerful are faint points.

Starlight is faint because so little of it falls into an eye’s small pupil. The cure is a bigger collector. A mirror curved inward like the bowl of a spoon, a concave mirror, reflects parallel rays so that they all meet at a focus. One a metre wide gathers about twenty thousand times more light than an eye. That is a telescope: a wide mirror or lens that collects faint light and brings it to a focus. In 1610 Galileo pointed an early one at Jupiter and found four moons that no eye had seen.

Light can also be led round corners. Inside a thread of very pure glass, light that strikes the wall at a shallow angle cannot escape. All of it bounces back in, an effect called total internal reflection. Bounce by bounce it follows the fibre for kilometres, as most internet traffic now does.