www.fransvanschooten.nl

 

Ibn al-Haytham

Ibn al-Haytham (965-1041), born in Basra (Iraq) made great progress in understanding the phenomenon of light. With experimental setups he examined the reflection of light in mirrors, not only flat, but also in curved or cone-shaped mirrors.

YouTube: Apparatus for the Observation of the Reflection of Light

A drawing tool to find reflection points

In 2013 I discovered a special drawing instrument in the Istanbul Museum of History of Science and Technology. Thanks to the support of Prof. Dr. Fuat Sezgin of the Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University, Frankfurt am Main, I was able to investigate its origin and operation.
In the winter issue of the Flemish periodical Uitwiskeling (2019 35/1) my article about a unique drawing instrument was published. For the Dutch society of mathematics teachers, I gave a workshop about this drawing tool. The drawing instrument supports you to playfully find the reflection points of an object in concave or convex mirrors. Like a neusis construction, it provides a good approximation, but lacks the mathematical exactness.

A publication in English and Turkish appeared in June 2019 at the The First International Prof. Dr. Fuat Sezgin History of Science in Islam Symposium.

  • ... a source of inspiration for modern highschool education ...

    In The 1st International Prof. Dr. Fuat Sezgin Symposium on History of Science in Islam Proceedings Book my contribution The Istanbul Museum of the History of Science and Technology in Islam as a Source of Inspiration for Modern High School Education: An Instrument for Finding Reflection Points is included. It shows how old instruments from a museum collection can be used for inspiring education.

    This link opens the PDF.

  • ... yansima noktalarini bulmak için bir araç.

    In The 1st International Prof. Dr. Fuat Sezgin Symposium on History of Science in Islam Proceedings Book my contribution The Istanbul Museum of the History of Science and Technology in Islam as a Source of Inspiration for Modern High School Education: An Instrument for Finding Reflection Points is included. It shows how old instruments from a museum collection can be used for inspiring education.

    This link opens the PDF with the Turkish translation.

  • Symposium 2019

    This is the link to the symposium website.
  • animation Marcolongo

    Use the animation to examine Marcolongo's instrument with different mirrors.

  • animation Leonardo Da Vinci

    Use the animation to examine Leonardo's instrument with different mirrors.

  • Bartin 2021

    This is the link to the lecture for the students of Dr I. Aslan Seyhan from Bartin University.


     
  • Symposium 2021

    At the The Second International Prof. Dr. Fuat Sezgin History of Science in Islam Symposium, I would like to talk about one of Ibn al-Haytham's experiments to visualise the reflection of light in concave and convex mirrors.

The problem comes back in different ways. Originally it was an optical problem. Below, there are four variations of the same problem.

  • Physicians might say: given a concave or convex circle, the position of a light source, the position of the eye of the observer, in which (multiple) positions in the mirror does the eye see the light source.
  • Sportsmen might say: given a round billiard, the position of a white billiard ball and the position of a red billiard ball, to which point or which points on the billiard belt you have to hit one ball so that the other ball becomes full.
  • A swimmer knowing the rule that he has to touch the edge of the swimming pool before picking up the ball would say: given my position and the position of the ball, where should I touch the edge to minimize my swimming distance.
  • Mathematicians might say: given two points, eye and light source, given a curve, in which points does the angle between the tangent to the curve and the line from eye to point of contact equals the angle between that same tangent line and the line from light source to point of contact. Common is that all three formulations are based on the law that states that the angle of incidence must be equal to the angle of rejection.

Common is that all formulations are based on the law stating that the angle of incidence must be equal to the angle of reflection.

The underlying mathematics is age-old. One author, for example, is Ptolemy (±100 − ±160) who wrote about reflection in his work Optica. Another author is Ibn Al Haytham (965−1040), also known in Europe as Alhazen. In the seventeenth century, Christiaan Huygens (1629−1695) addressed this problem. The mathematics of these men is too ambitious for most high school students.

 

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Drawing tool

In the Istanbul Museum of the History of Science and Technology in Islam a drawing tool has been exhibited to solve this problem in a practical way. According to the catalog, Marcolongo (1862−1943) was inspired by a drawing by Leonardo da Vinci (1452−1519). The text and the accompanying description of da Vinci is in the Codex Atlanticus. Careful study shows that the Marcolongo drawing tool is similar to that of Leonardo da Vinci, but there are also substantial differences.

The drawing instrument developed by Marcolongo is comprehensible to a wide audience. It is suitable for a practical lesson in which students produce the instrument themselves from cardboard and search for reflection points. An animation in Geogebra is on this web page.

jump to animation Marcolongo at this web page

The drawing instrument developed by Leonardo da Vinci is also suitable for a practical lesson. An animation in Geogebra is also on this web page.

jump to animation Leonardo Da Vinci at this web page

 

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Experiments of Ibn al-Haytham

Ibn al-Haytham was born in 965 in Basra in modern Iraq and died in Cairo around 1041. He wrote about many topics in astronomy, optics, and mathematics. Ibn al-Haytham has been praised for his breakthroughs in optics, as he was the first scientist who made big steps in this field since Ptolemy. Centuries later, scholars like Kepler, Snell, Beeckman and Harriot, who also worked in Optics, appreciated the mathematical character of the treatises of Ibn al-Haytham and considered him an important predecessor. According to [Smith, 2006, p. xvii] "Alhacen's experiment (to prove the equal-angles principle) is .. light-years beyond Ptolemy's in its instrumental and conceptual sophistication", and he made the major step "to determine precisely where on the surface of a convex or concave spherical mirror the radiation from a given object-point will reflect to a given center of sight."

Ptolemy had discussed the problem but he had limited himself to the easy case where the eye and the source of light are at the same distance of the center of a cylindrical mirror. The general case where the light and eye are not at the same distance of the center is far more difficult. Ibn al-Haytham solved it by a mix of practical experiments, conic sections, and rigorous mathematical proofs.

The phenomenon of light and the way in which we humans observe objects with our eyes is not straightforward. Nowadays there are plenty of textbooks and websites with educational movies, but these resources were not available in the time of Ibn al-Haytham, who had to figure out many things by himself. Moreover, he had to go against established beliefs. The working of the eye was still unknown, perfectly smooth mirrors were a luxury and cylindrical or spherical mirrors were not easy to obtain.

Ibn al-Haytham proposed the idea that light rays travel from an object to our eye in straight lines. He also understood the law of reflection stating that the angle of incidence equals the angle of reflection. He did, however, not yet have complete understanding of the laws of refraction, which specify the change of direction when for example light travels from water to air or from air to water. These rules had, however, been understood some decades earlier by al-'Ala' ibn Sahl, and were independently rediscovered in Europe by Snell and Descartes.

Nazif investigated manuscripts of Ibn al-Haythams Optics in 1942. He wrote an impressive transcription and commentary in Arabic. He added figures that help us to understand what kind of experiments Ibn al-Haythams did. Professor Sezgin reprinted Nazif's books, ordered to build a working setup based on these drawings. He also demanded a video of this setup. Everybody can watch this video at Youtube. Thanks to this video, it is immediately clear that Islamic scholars like Ibn al-Haytham should be praised for their contribution to the sciences.

YouTube: Apparatus for the Observation of the Reflection of Light

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Kamal al-Din Hasan ibn Ali ibn Hasan al-Farisi. (1309) Tanqih al-manazir, MS Istanbul, Topkapi Kütüphanesi, folio 167b-168a Risner, F. (1572). Opticae Thesaurus Alhazeni Arabis. page 184 Study of a convex circular mirror with center H, eye and object at A and B, four points of reflection at D, E, G and Z.

Drawing instrument

According to the catalog of the Istanbul Museum of History of Science and Technology in Islam, the instrument was invented by Leonardo da Vinci and elaborated by the Italian professor Roberto Marcolongo.

Wikipedia: Leonardo da Vinci

Wikipedia: Roberto Marcolongo

 

Exercises

The tasks below can be performed with the drawing tool.




 

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Animation Marcolongo

Use the slider to examine the different mirrors: flat, convex circle, concave circle, convex ellipse or concave ellipse. You can choose where the eye and the light source are situated with respect to the mirror. You can set the viewing direction with the movable point on the circle around the eye. With the buttons you can choose to make the drawing instrument visible or show the geometric location of the reflection points.

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Animation

The animation of the Marcolongo drawing tool is available in the GeoGebraTube

GeoGebra Marcolongo

 

Leonardo da Vinci

The website www.leonardodigitale.com shows much of the works of Leonardo da Vinci.

leonardodigitale.com

 

Source

The image below is the source of the transcription. The image has been taken from

leonardodigitale.com

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Text Leonardo da Vinci

Below is the original text of Leonardo da Vinci on the left and my translation into Dutch on the right. For the sake of clarity, all points in the text and in the figure are indicated with capital letters.

Colonna principale.
Due figure d'uno stesso strumento, con:
d - b - a - c ; d - b S - t o a - g - m n - f
Per trovare l'angolo della contingenzia per via di strumento. Sia adunque lo sperico dove si vede l'angolo della refressione ONM, e 'l punto A sia il luminoso e 'l B sia l'occhio e lo O sia l'angolo che si cerca, per vedervi il simulacro di tal luminoso. Ora piglierai una lista di legno sottile, larga men di mezzo dito, e sia DF, nella quale sia uno stretto canale, e questa, con una sottile agucchia o spilletto si fermi sopra il centro di tale cerchio ONM, passando per esso canale delle riga. Di poi congiugni due altri listelli equali infra loro, lunghi a tuo beneplacito, e questi si congiungano a uso di seste nel medesimo polo, che è stabilito nella fronte della predetta riga DF. E fatto questo, tu congiungerai la lista SG alla fronte della lista DS nel polo S, a mo' di sesto che s'apre e serra, e farali il suo canale, come facesti alla lista DF, e ferma un'agucchia nel luminoso A, che passi per il detto canale del listello SG. Ora tu hai a pigliare lo stremo del listello SG nel G e moverlo tanto in su e giu intorno al polo A (che, v' è il detto spilletto stabilito in loco del luminoso), che tu vedrai la circunferenzia del cerchio, nell' angolo della contingenzia O, fatto dalla divisione de' due listelli; e per gli angoli equali che si generano dentro al quadrato SBDO, si prova la perfezione dell' opera, cioè li angoli superiori sono infra loro equali, e li laterali sono equali infra loro, e 'l simile si conferma essere nelli angoli della contingenzia OT , eccetera. DO è messo infra l'occhio e 'l luminoso con altezza e vicinità all'occhio, e 'l luminoso a beneplacito perché non fa caso, pure che DS e DB sieno equali infra loro e che lo scontro finale delli 2 canali sien sopra la circunferenza del cerchio.

An instrument to find the angle of reflection by approximation. Given circular mirror OMN on which the reflection point must be found. Point A is the light source, point B is the eye and point O is the requested reflection point where the eye sees the image of the light source. Take a strip of thin wood DF of a half finger thick with a narrow slit. Put a needle in point C, the center of circle OMN. Let the needle fit in the slit DF. Attach two equally long strips, shorter than DF to each other in point D. These are the strips BD and DS. Join a long strip SG on point S. Put a needle in point A and let it fit in the slit of strip SG. Move point G, the end of strip SG such that the strips SG and DF intersect at a point on circle OMN.

The text of Leonardo da Vinci does not state that strip SG should be moved in such a way that point S is on the circle around point C through point B. However, that is expressly shown in his drawing.

Proof Leonardo da Vinci

Leonardo da Vinci provides a short mathematical proof. He claims that corresponding angles are equal to each other.

When point O has been found, to be precise, on the circumference of the mirror and point S lies on the circle around point C, the center of the mirror circle, through point B, the eye, then quadrilateral CBDS is a kite because the length of line segment BD equals that of line segment DS and the length of line segment CB equals that of line segment CS, from the nature of the construction. For every kite, diagonal OD is an angle bisector. Therefore angles BOD and SOD have the same size. Line COD passes through the center of the circle and thus is perpendicular to the tangent to that circle. Point A is on side OS. Therefore, the angles produced by lines OA and OB with the tangent line are also the same. Conclusion is therefore that in case the construction of point O has been completed, then the angle of incidence is equal to the angle of reflection. The eye in point B then sees in point O the image of the light source in point A.


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Animation Leonardo da Vinci

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Animation

The animation of the Leonardo da Vinci drawing tool is available in the GeoGebraTube

GeoGebra Leonardo da Vinci

 

 

 

 

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Sources

Astrolabes

The catalogue of the Collection of Instruments of the Institute for the History of Arabic and Islamic Sciences describes many ancient astrolabes and shows high quality pictures of replicas.

Geogebra

Catalogue of the Collection of Instruments

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 Dutch  Turkish