Where light bends: a water sphere and the rainbow

This lesson asks you to investigate how light is refracted as it passes through different media and to describe, in qualitative terms, how visible light is refracted at the edge between two media. The museum offers a medieval scholar's use of a water-filled glass sphere to study the path of light in a raindrop; your class carries out the investigation with blocks, water and measured angles. ¹

The expectations ask where the direction changes, and at what kind of edge. On a diagram of the sphere, mark each place where light passes from one medium to another.

Look closely at the model. Kamal al-Din al-Farisi replaced a tiny raindrop with a water-filled glass sphere to investigate light in a controllable model. Russell describes a dark room with one aperture, and an explanation of the primary rainbow by two refractions separated by one internal reflection. The secondary bow involves two internal reflections ². In an idealized drop, light entering water from air is refracted, reflected inside, then refracted again on exit ². The glass-and-water sphere is more complex than that ideal drop, because its vessel supplies extra refracting boundaries ³. Read the record of the water-sphere model, then mark on a sphere every place where the light passes from one medium to another.

Russell reports that al-Farisi came to Tabriz to study with al-Shirazi. Dissatisfied with answers to questions about refraction, he consulted his teacher. Al-Shirazi remembered a substantial book by Ibn al-Haytham and obtained a copy from a distant country ⁴. The record says this is the scholar's account of the introduction to the Tanqih, not a manuscript scene independently inspected by the museum ⁴.

The teacher's part in securing the book and encouraging revision is visible. Priority is another matter. MacTutor reports Boyer's preference for discovery by the teacher and elaboration by the pupil, alongside Rashed's objection to that attribution ⁵. The record keeps the disagreement and does not manufacture either an uncontested solitary inventor or a precisely divided joint project ⁵.

Colour marks a boundary of success. MacTutor describes his attempt to explain colour through the superposition of images on a dark background; Russell says the attempt was unsuccessful ^{6 2}. A successful account of paths can coexist with an unsuccessful account of why colours appear ^{6 2}. The record also does not award him the invention of the dark chamber itself ^{7 8}.

The record states the limits of what was read. The completion date of the Tanqih is disputed: one interpretation puts it before 1290, another after 1302 and before the teacher's death in 1311 ⁹. A later copy's date is not automatically the date of the experiment or its discovery ⁹. No original Tanqih manuscript or Hyderabad edition was inspected, and Russell's bibliography warns of textual and diagram errors in that edition ¹⁰.

Russell says al-Farisi explained the paths of light in the drop but that his attempt to explain colour was unsuccessful ². Take a position and answer the strongest objection to it: should a model that gets the path of the light right and the colours wrong still count as good science, and why?

• al-Farisi's water-sphere rainbow model: the two paths of light in the sphere, and what the sources say about colour.
• Kamal al-Din al-Farisi: the scholar who built the model.
• Tanqih al-Manazir: his critical revision of Ibn al-Haytham's Optics.
• Qutb al-Din al-Shirazi: the teacher, and the dispute over his part.
• Ibn al-Haytham's dark room: the earlier experiment with a hole and a dark room.

Read about al-Farisi's water-sphere rainbow model. Draw a circle for the sphere and trace one ray in, then mark each point where it enters, bounces or leaves.