In the catalogue of the collection of instruments of the Institute for the History of Arabic and Islamic Sciences, an apparatus is mentioned for the observation of the reflection of light. The idea of the apparatus is brought forward by Ibn al-Haytham, the eleventh-century scholar who has been praised for his breakthroughs in optics as he was the first scientist who made big steps in this field since Ptolomy. The apparatus gives experimental proof of the law of reflection. In his tract on optics, Ibn al-Haytham provided his mathematical proof. The apparatus covers the basic configuration of the experiment. In his mathematics, he dealt with all kinds of situations, as I mentioned in 2019. His predecessors limited themselves to the easy case where the eye and the source of light are at the same distance of the center of a cylindrical mirror. Ibn al-Haytham solved the far more difficult general case where the light and eye are not at the same distance of the center, using a mix of practical experiments, conic sections, and rigorous mathematical proofs.
The Istanbul Museum of the History of Science and Technology in Islam exhibits a precious new-build apparatus. Experiments with this replica were successful. One clearly sees the rays of light and the reflection of these rays in all kind of mirrors (flat, conical, spherical, etc..).
My paper discusses the mathematical and experimental works of Ibn al-Haytham and presents a lesson series. My aim is to develop a hands-on classroom lesson series using a low-cost 3D-printed apparatus to bring the optics of Ibn al-Haytham alive. The story is also about the advanced use of mathematics by Ibn al-Haytham, which goes far beyond high school mathematics. In my lecture, I would like to address the important role of the optics of Ibn al-Haytham and present an outline of that lesson series. Afterward, in a workshop, the apparatus and the lesson series can be demonstrated.
Design of our prototype
Our design is ready, first prototypes are printed, mirrors are folded, and tested.
Illustrations are from the catalogue of the collection of instruments of the Institute for the History of Arabic and Islamic Sciences.
Our experiment proves that this setup of the apparatus does work. Next step is to develop a low cost reliable 3D printed version of this apparatus that is suitable for classroom demonstrations. Light source will be a cellphone! So every student can do this experiment with his own device!
In his treatise On the Shape of the Eclipse, Ibn al-Haytham investigated the image of a crescent solar eclipse through a pinhole of a camera obscura. Since 1940, a small group of authors elaborated on Ibn al-Haytham's texts, to name a few: Nazif, Sabra, Smith and Raynaud. Since the fifteenth century, Western scholars tried to master the topic but it took until the seventeenth century before their were right solutions.
Nazif presented an interesting drawing with multiple cones. In order to emphasize these cones, color is added in the right picture.
In his critical edition of Ibn al-Haytham's Eclipse, Raynaud presented drawings from a selected number of manuscripts of Ibn al-Haytham.
All above images show three upside down crescents, while Gemma Frisius only mentions one crescent in his book in 1545.
One century later, in 1671, père Chérubin d' Orléans presented a drawing with three cones`, but for some reason, the straight lines are broken in the aperture. According to the text there is no lense, but the broken lines do suggest lenses.
Mihas published his article A Historical Approach to the Teaching of the Linear Propagation of Light, Shadows and Pinhole Cameras in 2005. He presented the same three cones and a computer simulation to predict the final shape: the image of a crescent looks like a peach!
Raynaud did computer simulations too. The result being the same: the image of the crescent looks more like a peach than a croisssant. My simulation shows similar results. The top rows show the crescent, the bottom row the image at 2500 mm distance and aperture diameter 11 mm.
The image of the eclipse becomes much better with a smaller aperture of radius 1 or 2 mm.
Thousand years ago, Ibn al-Haytham investigated the shape (image) of a crescent solar eclipse through a pinhole of a camera obscura. For a large aperture, the shape looks distorted. To explain this phenomenon, you have to understand that the sun has a width, namely an arc angle of half a degree. Ibn al-Haytham proposed a point-by-point construction to determine for each and every point which lightrays produce the shape. For every point, the amount of light is the addition of all the rays that come together in that single point, and all the points together produce the entire shape.
The animation shows the image of the letter F on a wall when it is lit by a huge halogen light bulb at a near distance. The experimental setup uses a metal sheet in which the letter F has been cut out. So, light falls through the F, and light is blocked by the frame. The question is what will be the image of the letter F on the outer wall? Is it an F, or will it be an inverted F? Will one see the contours of the F? Will one see the shadow of the frame around the F?
Ibn al-Haytham explains that one should produce a real pointwise construction to obtain valid results. Purpose of this animation is to visualize this pointwise approach.
The animation shows the halogen light bulb and a point moving along a spiral in that lamp. It creates a rectangular grid over the F and its frame. It draws rays from hundreds of points on this spiral to all the points in the grid. It generates thousands of rays for an accurate view.
Solar Eclipse on 10 June 2021
There was a solar eclipse on 10 June 2021. We were curious to develop a low-cost experiment to take pictures of this eclipse. The first attempt was with binoculars that we had mounted in a banana box. We projected the sunlight onto a second box, covered with white paper. The image through the binoculars was sharp and clear. In the Netherlands, the eclipse was only partial. Notice that the bite that the moon takes from the sun is at the top.
We were warned that the intensity of the sunlight can damage binoculars. Besides, good binoculars are not cheap. Therefore, we did a second experiment.
The second attempt was with waste material like a cardboard tube one meter long and five centimeters in diameter. The tube was masked off with duct tape to a small opening of one mm. The image was about one cm in diameter, less sharp, and less bright but the contour of the eclipse is visible. Notice that the bite that the moon takes from the sun is at the bottom. The experimental setup produces a top-down / left-right image. The camera software decided that the color of the shade was blue. The costs of this experiment were limited to a tripod, waste material, and duct tape. Still, the experimental results were of sufficient quality: one could clearly see the image of the solar eclipse, but of course, fainter.