Light in a drop of water

Trace a ray into a drop, off its back surface and out again. At each boundary ask whether the light bends, reflects or does both. Then ask what about the colours would still need explaining.

Follow a ray into a drop that is not a drop. Kamal al-Din al-Farisi replaced a tiny raindrop with a water-filled glass sphere to investigate light in a controllable model ². In an idealized drop, light entering water from air is refracted, reflected inside, then refracted again on exit. The primary path has one internal reflection; the secondary path has two between entry and exit ². The glass adds boundaries a drop does not have: MacTutor says al-Farisi examined the approximation and considered the glass contribution negligible for his purpose ³. The editor of the Manazir says optics in Ibn al-Haytham's hands studied light's three conditions: rectilinear radiation, reflection and refraction ⁴.

Russell reports a reason from al-Farisi's own setting. He came to Tabriz to study with al-Shirazi, possibly before 1290. 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 ⁵. This is the scholar's account of the introduction to the Tanqih, not a manuscript scene independently inspected by the museum ⁵.

Who deserves the credit, the teacher or the pupil? MacTutor reports Boyer's preference for discovery by the teacher and elaboration by the pupil, alongside Rashed's objection to that attribution ⁶. The record retains the disagreement, and does not claim to have compared every underlying study ⁷. The completion date is also disputed: one interpretation puts it before 1290, another after 1302 and before the teacher's death in 1311 ⁸.

A model that gets the paths right need not get the colours right. MacTutor describes al-Farisi's attempt to explain colour through the superposition of images on a dark background, and Russell says the attempt was unsuccessful ^9 2. A successful account of paths can coexist with an unsuccessful account of why colours appear ^9 2. The second bow is not adequately described as a copy of the first after an external mirror: a changed internal path is part of the explanation ².

The record rests on MacTutor, Russell's article and the Science Museum's, and it says the full Rashed paper could not be downloaded, so only its opening was read. No original Tanqih manuscript or Hyderabad edition was inspected, and Russell's bibliography warns of textual and diagram errors in that edition ¹⁰. Ask how much of what you have read about the sphere comes from al-Farisi's own pages, and how much from three modern accounts of them.

Russell says al-Farisi's attempt to explain colour was unsuccessful, while his explanation of the light paths is credited. Does a model that explains one part of a phenomenon count as an explanation of it, and how would you answer the objection that colour is the part of a rainbow most people notice?

• Al-Farisi's water-sphere rainbow model: the two light paths and the glass that stands in for a drop.
• Optics: the three conditions of light the Manazir studies.
• Kamal al-Din al-Farisi: the scholar, and the dispute over his teacher's part.
• Tanqih al-Manazir: his critical revision of Ibn al-Haytham's book.