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Shape of the Eclipse

Author:Henk Hietbrink
Topic:Geometry

Solar Eclipse and Crescent Moon

A solar eclipse is a magnificent event. Even during a full eclipse, the sunlight is so bright that one may hurt his eyes. Mankind thought of all kinds of devices to investigate the shape of the eclipse. The crescent moon is of interest too. Nowadays with modern equipment, there are plenty of high-quality pictures, but in the old times, it was much more difficult to study the shape of the eclipse or the crescent. Distortions did happen and were hardly understood.

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. 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. 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 light rays 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. link: https://www.fransvanschooten.nl/camera.htm#geogebra

What does it do?

The animation has buttons, a graphic to create the eclipse and sliders to define the size of the camera obscura.
  • [ Eclipse Pointwise ] generates a grid of points of the eclipse. These points are used in the creation of the shape.
  • [ Shape Pointwise ] generates a grid of points of the shape. For each point of the aperture, the number of pointwise generated light rays are counted. The higher the count, the more bright yellow the color of that imagepoint, the lesser, the more dim.
  • [ Shape Contour ] generates the shape in another way. The boundary of the aperture is drawn as a white circle. A dot spirals within the aperture marking each point as a center of an image of the sun (eclipse) or the moon (crescent). All images together make up the shape of the eclipse. The red circle shows the border of the image.
  • [ Delete ] clears the screen.
A longer description is available below the animation.
Use the sliders to define:
  • width of the aperture in millimeters
  • distance between the aperture and the projection screen
  • number of grid points per millimeter
The idea behind the animation is that some points of the shape are touched by many sun rays and other points by none or only a few. [ Shape Pointwise ] counts the number of sunrays. The coloring scheme is relative to the maximum number of sunrays of a specific configuration. As a result, the brightest yellow is used for both a small crescent as a limited eclipse. This way, the animation emphasizes the pointwise approach of Ibn al-Haytham, taking into account that central points are touched more often than points at the boundary of the image. The button [ Shape Contour ] does not take into account these frequencies. The image is created by superimposing a lot of crescents. The technique behind [ Shape Contour ] is basically a GeoGebra animation of a moving boundary and therefore quite fast. The spectator sees a moving eclipse and does not notice the computational effort. [ Shape Pointwise ] generates a matrix of points, each of them colored according to the calculated frequency of the touching rays. The spectator has to wait until the whole drawing is ready. He does notice the computational effort and may become impatient. For those who want high-resolution images with many grid points per mm, the advice is to download the GeoGebra file and do all computations in the GeoGebra standalone edition. More information is on my website https://www.fransvanschooten.nl/camera.htm#geogebra

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