Ibn al-Haytham

His masterwork is the Kitāb al-Manāẓir, the Book of Optics, written in Cairo, probably in his later years, about 1028 to 1038. It is a full account of seeing in seven books, arranged by the path light takes to reach the eye.

Books one to three cover direct sight: how light and colour travel, how the eye is built, how we judge what we see, and how sight can be fooled. Books four to six cover light that reaches the eye after bouncing off a mirror, the study of reflection. The seventh book covers refraction, the bending of light as it passes from one clear substance into another, such as from air into water.

The plan follows Ptolemy's Optics, written in the second century. What Ibn al-Haytham changed was the foundation: what actually travels between the eye and the things it sees.

Do our eyes reach out to the world, or does the world reach in to our eyes? The question divided scholars for well over a thousand years.

Mathematicians such as Euclid and Ptolemy explained sight with visual rays: straight lines that leave the eye and spread out in a cone, with its tip at the centre of the eye and its base on whatever is seen. The picture turned seeing into geometry.

Natural philosophers in Aristotle's tradition held the reverse, that something passes from the object into the eye. Ibn al-Haytham opens the Book of Optics with this old disagreement between the mathematicians and the natural philosophers. Rather than simply pick a side, he set out to rebuild the subject from observation, keeping what each side had right.

Ibn al-Haytham began with things anyone can check. Look straight at the sun and your eyes hurt so much that you cannot keep them open. Gaze for a while at a white wall in bright daylight, then turn to a dark place or shut your eyes, and a glowing patch of the same shape stays in view before it fades. Stare at a sunlit meadow, then look at something white in the shade, and the white looks tinged with green.

These lingering images, now called afterimages, show that light acts on the eye. The eye is on the receiving end: bright light affects it, can hurt it, and leaves a mark that takes time to fade. Nothing in these cases requires anything to leave the eye, so he built his account of sight on light coming in.

Light coming in raised a puzzle. Every point of a lit object sends light out in all directions, so light from every point reaches every part of the eye. Why do we see a clear picture instead of a blur?

His answer kept the mathematicians' geometry and reversed its direction. From each point of the object, only one ray meets the surface of the eye head-on, at right angles, and passes on toward the eye's centre without bending. Only that perpendicular ray counts, because it strikes the eye most forcefully; the oblique rays strike too weakly to be sensed. One such ray arrives from every point, and together they form a cone of straight lines with its tip at the centre of the eye: the old cone of visual rays, now running inward. Point by point, the object is laid out in the eye in its proper order.

To show how light travels, he described a test for any dark night. Set several lamps outside a room, go in and close the door, leaving only a narrow gap. On the wall facing the gap appear separate spots of light, one for each lamp, each on a straight line drawn from its lamp through the opening. Screen one lamp and only its spot vanishes; uncover it and the spot returns.

So light travels in straight lines, and the beams of many lamps can cross in one small opening and still arrive separately. A dark room lit through a small hole was later named a camera obscura. Pinhole images had been noticed long before, but Ibn al-Haytham made such rooms and openings into instruments for careful, repeatable tests.

Ibn al-Haytham set out his method at the start of the Book of Optics. First survey many particular cases and draw general rules from them by induction; then reason forward step by step, criticising premises and staying cautious about conclusions. He then made sure of each rule by testing claims by experiment, a practice he called iʿtibār.

For the rule that sight works only along straight lines, he fixed a straight hollow tube to a ruler and looked through it at an object. Cover part of the opening, and exactly the part of the object in line with it disappears.

The word iʿtibār came from astronomy, where it meant testing past observations against new ones. In optics it came to mean a test with equipment built for the purpose. His translator A. I. Sabra calls this a significant conceptual development in the history of experimental science.

Books four to six turn to mirrors. Ptolemy had already stated that light leaves a mirror at the angle it arrives at, but for rays from the eye. Ibn al-Haytham designed a test that used light itself.

He described a hollow wooden cylinder with narrow holes bored through its wall, all aimed at a small mirror in the middle. Sunlight let in through one hole makes a bright spot on the inner wall, exactly where the hole on the opposite side is aimed. He applied the test to seven kinds of mirror: one flat, three curving outward and three curving inward. In his account the angles always come out equal, and the incoming ray, the outgoing ray and the line perpendicular to the mirror all lie in one flat plane. The historian A. Mark Smith doubts that apparatus so precise could be made in his day.

The seventh book takes up refraction. Ibn al-Haytham described a bronze disc marked in degrees, hung in a vessel of water and turned toward the sun, so that the new direction of a thin beam entering the water could be read off the rim. He gave the same method for air into glass and glass into water.

He stated the results as rules. Light passing into a denser substance bends toward the perpendicular, so its angle from that line is always smaller than the angle at which it arrived; passing out into a thinner substance, it bends away. The closer to head-on the light arrives, the less it bends. Yet for all that careful description he gave no table of measurements, and Smith concludes that he probably never ran the tests as described but set them out as carefully contrived thought experiments.

How far a beam bends depends on what it enters. Send light into water at 60 degrees from the perpendicular and it continues at about 41 degrees; send it into ordinary glass and it continues at about 35. Glass bends light more than water does.

Ibn al-Haytham described the bending only in words, as a set of rules. The exact law of refraction had in fact been found around 984, some fifty years before the Book of Optics, by Ibn Sahl, a mathematician at the court in Baghdad, in a treatise on burning mirrors and lenses. Ibn Sahl used it to design lenses that bring light to a sharp focus. Ibn al-Haytham did not take it up, and in Europe the same law was found again in the 1600s and named after Willebrord Snell.

A full moon rising behind rooftops looks enormous; hours later, high overhead, it looks small. Yet measured as an angle it is the same size in both places, about half a degree across. Ptolemy had discussed the puzzle, and Ibn al-Haytham ends the Book of Optics with it.

First he showed that the bending of light by the air is far too slight to explain it. Then he argued that we judge an object's size from two things together: the angle it fills in our view and how far away it seems. We see the sky not as a dome but as a flattened ceiling, so the moon near the horizon seems much farther away than the moon overhead. The same angle at a greater apparent distance is judged to be a bigger moon. This is the moon illusion, and he placed its cause in perception, not in the sky.

Ibn al-Haytham admired Ptolemy and followed his plan in the Book of Optics, yet he also wrote a book about Ptolemy's faults: al-Shukūk ʿalā Baṭlamyūs, the Doubts concerning Ptolemy. It went through the Almagest, the Planetary Hypotheses and the Optics, showing where they contradicted themselves or the nature of real bodies. Some of Ptolemy's planetary models, for example, needed a heavenly sphere to turn evenly around a point that was not its own centre, which no real sphere can do.

He explains his purpose at the start. God has not protected scientists from error, he writes, so the seeker after truth does not simply trust the writings of the ancients. He questions what he reads and submits to argument and demonstration. He must suspect himself as well, so that he falls into neither prejudice nor leniency.

In the Muslim world the Book of Optics found few close readers, the great exception being Kamāl al-Dīn al-Fārisī, who revised it in the early 1300s. A Latin translation, made in the late twelfth or early thirteenth century and titled De aspectibus, became the main source for Roger Bacon, John Pecham and Witelo in the 1260s and 1270s. Their books made its theory Europe's standard account of light and sight until the 1600s. In 1572 Friedrich Risner printed it in Basel.

In 1604 Johannes Kepler presented his own optics as a mere supplement to Witelo, yet on the eye he broke with the tradition. Ibn al-Haytham had placed sensing at the front of the eye's lens, with the picture kept upright; Kepler showed that the lens focuses an inverted image onto the retina, just as a small hole casts one on the wall of a dark room.