It comprises drawing lines from two points in the plane of a circle meeting at a point on the circumference and making equal angles with the normal at that point. This is equivalent to finding the point on the edge of a circular billiard table at which a player must aim a cue ball at a given point to make it bounce off the table edge and hit another ball at a second given point. Thus, its main application in optics is to solve the problem, "Given a light source and a spherical mirror, find the point on the mirror where the light will be reflected to the eye of an observer. His method can be readily generalized to find the formula for the sum of any integral powers, although he did not himself do this perhaps because he only needed the fourth power to calculate the volume of the paraboloid he was interested in. He used his result on sums of integral powers to perform what would now be called an integration , where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid. His solution was extremely long and complicated and may not have been understood by mathematicians reading him in Latin translation.
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Book of Optics Kitab Al-Manazir Ibn Al-Haytham Alhazen AD —21 The greatest physicist of the medieval era led a life as remarkable as his discoveries were prodigious, spending a decade in prison and at one point possibly feigning mental illness to get out of a tight spot. His greatest and most famous work, the seven-volume Book of Optics Kitab al-Manathir hugely influenced thinking across disciplines from the theory of visual perception to the nature of perspective in medieval art, in both the East and the West, for more than years.
The Babylonians, Egyptians and Assyrians all used polished quartz lenses. The basic principles of geometric optics were laid down by Plato and Euclid. They included ideas such as the propagation of light in straight lines, and simple laws of reflection from plain mirrors. As a young man, Ibn al-Haytham received an excellent education and was widely noted as a mathematical and scientific prodigy. Frustrated by his administrative duties working in a government post in the vast Islamic Empire — which at the time stretched from India to Spain — he was sacked owing to real or, as some speculate, faked mental illness.
Sometime during the first decade of the new millennium, he proposed an ambitious project to dam the Nile. However, on seeing the scale of the task, Ibn al-Haytham quickly realized that it was beyond him. Far from cowing him, the decade of imprisonment granted Ibn al-Haytham the seclusion to think and write, particularly on optics.
After his release around the year , he began working at a prolific rate, carrying out a series of famous experiments on the nature of light. For example, using a camera obscura, he proved that light travels in straight lines; he also mathematized the fields of catoptrics reflection of light by mirrors and dioptrics refraction of light through lenses.
This huge body of experiment and theory culminated in his Book of Optics. In it, Ibn al-Haytham gives detailed descriptions of his experiments, such as exploring how light rays are reflected off plain and curved surfaces. He includes the apparatus he used, the way he set it up, the measurements and his results. He then uses these observations to justify his theories, which he develops with geometrical models. He even urges others to repeat his experiments to verify his conclusions.
Many historians of science consider Ibn al-Haytham to be the first true proponent of the modern scientific method. The Greeks had several theories. In the fifth century BC, Empedocles had argued that a special light shone out of the eye until it hit an object, thereby making it visible. This became known as the emission theory of vision. Several centuries later, Ptolemy expanded on this idea. Early Islamic scholars such as al-Kindi and Hunayn ibn Ishaq favoured a combined emission—intromission theory.
They posited that the eye sends out light to the observed object, which then reflects the light back into the eye. If it does not, how can the eye perceive what its rays have fallen on? Light must be coming back to the eye, and this is how we see.
But if so, what use is there for the original rays emitted by the eye? The light could come directly from the object if it is luminous or, if it is not, could be reflected from the object after being emitted by another source.
Rays from the eye, decided Ibn al-Haytham, are an unnecessary complication. He also went further than anyone before in trying to understand the underlying physics of refraction.
He argued that the speed of light was finite and varied in different media, and he used the idea of resolving the path of a light ray into its vertical and horizontal components of velocities. He carried out all his work geometrically, and introduced many new ideas, such as the study of how the atmosphere refracts light from celestial bodies.
Al-Farisi, who wrote The Revision of the Optics Tanqih al-Manazir , used geometry to arrive at the first correct mathematical explanation of the rainbow at the same time as, but independently of, the German scholar Theodoric of Freiberg. The Book of Optics was first translated into Latin in the late twelfth or early thirteenth century, as De Aspectibus. The English philosopher and empiricist Roger Bacon then wrote a summary of it, as did his Polish contemporary Witelo.
It was soon being cited across Europe. De Aspectibus was translated into Italian in the fourteenth century, making it accessible to practitioners such as the Florentine art theorist and architect Leon Battista Alberti, author of the treatise On Painting Della pittura , the sculptor Lorenzo Ghiberti and the geometer-artist Piero della Francesca.
These revolutionary artists strove to understand both the objective world and the visual system that determined its appearance. Today, as we use laser beams to manipulate atoms, stimulate neurons with light or convey information in entangled photons, it is worth recalling that the foundations of this field were laid down around 1, years ago by Ibn al-Haytham.
Vision theory[ edit ] Before the Book of Optics was written, two theories of vision existed. The extramission or emission theory was forwarded by the mathematicians Euclid  and Ptolemy ,  who asserted that certain forms of radiation are emitted from the eyes onto the object which is being seen. When these rays reached the object they allowed the viewer to perceive its color, shape and size. An early version of the intromission theory, held by the followers of Aristotle and Galen , argued that sight was caused by agents, which were transmitted to the eyes from either the object or from its surroundings. Al-Haytham offered many reasons against the extramission theory, pointing to the fact that eyes can be damaged by looking directly at bright lights, such as the sun.
Alhacen argued on the basis of common observations such as the eye being dazzled or even injured if we look at a very bright light and logical arguments such as how a ray could proceeding from the eyes reach the distant stars the instant after we open our eye to maintain that we cannot see by rays being emitted from the eye nor through physical forms entering the eye. Through his extensive research on optics, he has been hailed as the "father of modern optics". The eye perceives the size, shape, transparency color and light , position, and motion from cognitive distinction which is entirely different from perceiving by mere sensation the characteristics of the object. The faculty of the mind, for Alhacen, includes perceiving through judgement and inference of distinct properties of similar objects outline and structure. Alhacen continues this body of work by concluding that the discrimination performed by the faculty of judgment and inference is in addition to sensing the objects visible form and not by pure sensation alone. We recognize visible objects that we frequently see.
Ibn Al-Haytham and the Legacy of Arabic Optics
Book of Optics Kitab Al-Manazir Ibn Al-Haytham Alhazen AD —21 The greatest physicist of the medieval era led a life as remarkable as his discoveries were prodigious, spending a decade in prison and at one point possibly feigning mental illness to get out of a tight spot. His greatest and most famous work, the seven-volume Book of Optics Kitab al-Manathir hugely influenced thinking across disciplines from the theory of visual perception to the nature of perspective in medieval art, in both the East and the West, for more than years. The Babylonians, Egyptians and Assyrians all used polished quartz lenses. The basic principles of geometric optics were laid down by Plato and Euclid. They included ideas such as the propagation of light in straight lines, and simple laws of reflection from plain mirrors.