Abu ‘Ali al-Hasan bin al-Hasan bin al-Haytham

Alhazen . Abu ‘Ali al-Hasan bin al-Hasan bin al-Haytham, known in the western world as Alhazen or Alhacen. Arab physicist born in Basra , part of what is now Iraq, in the year 965 and, after a fruitful life and enormous scientific contributions, died in Cairo , Egypt in the year 1039 . Sometimes called al-Basri, which means from the city of Basra, in Iraq, and at other times called al-Misri, which means from Egypt.


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  • 1 Biographical synthesis
    • 1 Contributions
    • 2 Death
  • 2 The Alhazen problem
  • 3 Sources

Biographical synthesis

Alhazen was born in Basra , part of what is now Iraq , in the year 965 ; he received education in Basra and Baghdad . Sometimes called al-Basri, which means from the city of Basra, in Iraq, and at other times called al-Misri, which means from Egypt .

Bin al-Haytham was attracted to scientific studies and dedicated more time to them than to religious reflections, thus he decided to turn his energies to mathematics and physics .

Alhazen, in an attempt to gain a good reputation, assured that he would discover a machine that would regulate the floods of the Nile. As expected, this caught the attention of the Egyptian caliph, who assigned the project to him.

Unfortunately for Alhazen, the then Egyptian caliph was al-Hakim, the most dangerous reign to have existed between the time of Caligula and [Ivan the Terrible]]. Alhazen was greatly influenced by the fact that al-Hákim was not joking that the machine should be built immediately or else he would pay for it with some deliberate and long sentence.

Alhazen had no choice but to pretend to have gone mad, a comedy that he maintained until al-Hakim’s death in 1021 . In those moments when Alhazen could safely demonstrate his sanity, he manifested himself as one of the most important physicists of the Middle Ages .


Bin al-Haytham lived many of his years near the Azhar Mosque in Cairo, where he did his scientific research and worked as a teacher. The writings that he left are very numerous, it is said that he made about 92 works. The subjects of his preference were astronomy, mathematics and optics, from which he did research on the theory of light and developed a theory of vision.

He wrote a seven-volume series on optics called Kitab al-Manazir, which is perhaps Bin al-Haytham’s most important contribution. In 1270 it was translated into Latin under the name Opticae thesaurus Alhazeni. In the introduction the author expresses that he is initiating an investigation of principles and premises where he will try to include critical foundations and caution when expressing conclusions. He affirmed that he would seek to use justice, that he would not allow himself to be carried away by prejudices and that he would seek to seek the truth without being carried away by opinions.

He also built parabolic mirrors, used in telescopes. Like Ptolemy, he thought that the atmosphere had a finite thickness, which would be about ten miles.

In the first volume he establishes that his research on light will be based on experimental evidence rather than abstract theories. He affirms that light is the same, regardless of the source from which it comes, and gives as examples the light of the sun, the light emitted by fire or that which is reflected by a mirror; all – he affirms – are of the same nature.

Alhazen is the first scientist to offer the correct explanation of vision by showing that light is reflected from objects to the eye. He was the first to describe the parts of the eye in a specific way and although he does so in an erroneous way, because he did not conceive the existence of a lens in the ocular structure, he established criteria that would serve as the basis for future scholars of the subject.

He dared to contradict the theories of vision of Ptolemy and Euclid , who held that vision results from a beam of light that emerges from the eye and reaches the object. Instead, he correctly postulated that all points on an object or an illuminated area radiate rays of light in all directions, but only one ray from each point reaches the eye perpendicularly, while the other rays reach the eye. different angles and cannot be seen. He is considered, for all this, as the father of modern optics.

He tried to explain binocular vision and was correct in his explanation of the apparent enlargement of the sun and the moon when they are close to the horizon.

His research in the field of optics led him to propose the use of the camera obscura, becoming the first scientist to mention this artifact; By means of this, he was able to form an inverted image of a luminous object allowing the light to pass through a small hole. Without a doubt, this scientist was the greatest authority of the Middle Ages. Researchers who were later influenced by his work include Roger Bacon , Johannes Kepler, and Isaac Newton .

In another of his works, he analyzes visual perception, the conditions necessary to achieve good vision, and the conditions that cause visual problems. He also approached, with a mathematical spirit, the theory of reflection.

He made a careful examination of the passage of light through various means and discovered the laws of refraction. He carried out the first experiments on the decomposition of light into its constituent colors. His work Kitab-al-Manazir was translated into Latin during the Middle Ages . He made extensive lectures about various physical phenomena such as shadows, eclipses, the rainbow, and speculated about the physical nature of light.

Alhazen also examined visual problems caused by reflection and analyzed refraction. His research in optics focused on spherical and parabolic mirrors and spherical aberrations. He made the important observation that the radius between the angle of incidence and refraction does not remain constant and investigated the magnifying power of lenses.

In one of his books, he discussed the density of the atmosphere and conceived a relationship between it and its height. By studying atmospheric refraction he concluded that twilight ceases until the sun is 19 degrees below the horizon line and, on this basis, he measured the height of the atmosphere, concluding that it was 15 kilometers, which in reality is the height of the troposphere , the part of the atmosphere closest to the Earth’s surface .

In the same way, he delved into the theories of attraction of masses and was apparently aware of the acceleration factor due to gravity.

Among other works on optics by Alhazen, we can mention a study on the light of the moon , in which he observes that the moon shines as if it were an object with its own light even though it only reflects sunlight . He also has studies on the halo, the rainbow; over fiery paraboloidal mirrors and fiery spheres.


After a fruitful life and enormous scientific contributions, he died in Cairo , Egypt in 1039

Alhazen’s problem

In book V of this Arab thinker appears the statement of a problem that has attracted the attention of many scholars through the centuries, the questioning says: “Given a source of light and a spherical mirror, find the point in the mirror of where the light will be reflected towards the eye of an observer. ”

Actually the problem is exposed by Alhazen considering also cylindrical and conical mirrors. In the aforementioned volume V, Bin al-Haytham offers a detailed description of the geometric solution of the problem.

Although its solution is not very important in modern optics, it is interesting to know that a great number of thinkers have tried to clarify it throughout history.

It is actually a problem formulated by Ptolemy in the year 150 ; it asks to find a method to obtain the point in a spherical mirror where a ray of light is reflected from a source towards an observer.

It is also known as “The Alhazen billiard problem” since it can also be posed like this: find the point on the perimeter of a round billiard table where you have to aim the cue ball to make it bounce once outside the perimeter of the table and hit another ball at a second given spot.

The solution leads to a fourth degree equation that can be represented like this:

H (x2 – y2) – 2K xy + (x2 + y2) (hy – kx) = 0

This problem is equivalent to determining the point on a spherical mirror where a ray of light will be reflected to go from a given source to an observer.

The problem is impossible to solve using compass and squares, since the solution requires the extraction of a cube root. Alhazen describes his solution in a confusing and unclear way in the fifth book of his “Opticae Thesaurus”.

One of the historical personalities who tried to solve it was Leonardo Da Vinci , who recognized that he would not achieve it geometrically and resorted to a mechanical solution, proposing the construction of an articulated apparatus, a kind of pantograph that is indicated as one of the first instruments. history calculation.

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