Al-Farisi's water-sphere rainbow 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. This was more than treating a cloud as a mirror, but it was not a successful modern physical theory of colour ¹.

The investigation belongs to the Tanqih al-Manazir, his critical revision of Ibn al-Haytham. This record distinguishes successful light paths from an unsuccessful colour explanation, and retains debate over the contribution of his teacher, Qutb al-Din al-Shirazi. It does not award priority for all optics or for inventing the dark chamber itself ^{2 3}.

This is an experimental and geometrical model, not a weather-making machine. An individual raindrop is difficult to isolate; a larger sphere offers a way to investigate entry, exit and internal reflection. That does not make the vessel identical to a drop: the glass introduces additional refracting boundaries, a limitation explicitly discussed in the account read here ⁴.

The two bows are not simply decorative lines. The modern photograph shows a brighter inner bow and a fainter outer one with reversed colour order, but it is not a measurement of al-Farisi's experiment. The Science Museum explains the one-reflection and two-reflection paths while distinguishing Newton's later explanation of the constituents of white light ⁵.

Russell describes al-Farisi bringing together Ibn Sina's observation that a bow need not depend on dark clouds and Ibn al-Haytham's investigations of refraction and transparent spheres. The ingredients were not created from nothing. Respect for a predecessor did not prevent revision, and an observation about droplets is not evidence that Ibn Sina had already supplied the entire later model ⁶.

In the earlier explanation discussed by MacTutor, a cloud reflected sunlight toward the eye. Moving attention inside the drop created a different question that could be examined with a model. A weakness in one explanation is not a judgement against all Ibn al-Haytham's optics, still less against every experiment before al-Farisi ⁷.

Russell reports that al-Farisi came to Tabriz to study with al-Shirazi, possibly before1290. 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. This is the scholar's account of the Tanqih's introduction, not a manuscript scene independently inspected by the museum ⁸.

The completion date is disputed: one interpretation puts it before1290, another after1302 and before the teacher's death in1311. The record therefore retains a thirteenth-to-fourteenth-century horizon instead of choosing an unsupported exact1309. A later copy's date is not automatically the date of the experiment or its discovery ⁹.

MacTutor explicitly identifies al-Farisi as an Islamic mathematician, providing individual evidence for Muslim identity. The museum's separately declared Sunni frame is not a personal denominational certificate inferred from nationality, name or teacher. The biography gives birth about1260 and death about1320 at Tabriz; these remain approximate, without an invented Hijri equivalent or exact day ¹⁰.

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. We retain the disagreement rather than manufacture either an uncontested solitary inventor or a precisely divided joint project ¹¹.

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. 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 ¹.

For teaching, let T denote crossing the boundary with refraction and R internal reflection. The paths become T-R-T and T-R-R-T. Each contains two boundary crossings, but their reflection counts differ. These are modern explanatory symbols, not letters transcribed from the manuscript. Nor are they a complete diagram specifying angles, intensity or wavelength.

The glass-and-water apparatus is more complex than that ideal drop. Its vessel supplies extra refracting boundaries. MacTutor says al-Farisi examined the approximation and considered the glass contribution negligible for his purpose. This reports his reasoning; it does not establish that every vessel can be ignored in every experiment or that any sphere gives identical results ¹².

Colour marks a boundary of success. MacTutor describes his attempt to explain it through the superposition of images on a dark background; Russell says the attempt was unsuccessful. We do not silently substitute modern physics and call it his theory. A successful account of paths can coexist with an unsuccessful account of why colours appear ^{13 1}.

Russell finds no evidence of a Latin translation of al-Farisi, while comparing his investigation with Theodoric of Freiberg's. The Science Museum presents parallel experiments and the influence of Ibn al-Haytham on both. These are the accounts consulted, not the result of a museum search through every archive that proves every possible contact impossible ^{14 15}.

Russell also describes the Tanqih carrying optical material to later figures, including Taqi al-Din ibn Maruf. Mention of a reader does not establish that every passage in that reader's work came from the rainbow experiment. Transmission of a book and transmission of a particular argument are different questions, each requiring evidence ¹⁴.

The dark chamber provided controlled light; this record does not claim that al-Farisi invented it. The transparent sphere combined reflection and refraction questions whose elements Ibn al-Haytham had investigated. Russell describes a constructive reworking of inherited tools and results, rather than a merely verbal gloss or repetition of an earlier conclusion ¹⁶.

Droplet observations also mattered. If a dark cloud was not indispensable, defining that cloud as a mirror was not enough. This change in question does not amount to a modern account of every property of light. Seeing colours through an apparatus is not evidence that its maker measured wavelengths or possessed a modern spectral theory ¹⁷.

The Tanqih extended beyond a revision of seven optical books, with a sequel and appendices addressing further questions. Russell's account makes clear that its importance was not confined to classroom commentary. That does not make every section a rainbow explanation or turn investigations of shadows, eclipses and the burning sphere into alternative names for this contribution ³.

Historians can compare paths in different authors without proving borrowing. When the Science Museum introduces Newton's treatment of white light, it shows a change in understanding, not a theory already demonstrated in the Tanqih. Shape, reversed colour order and the physical nature of colour need to remain distinguishable questions ^{18 1}.

A familiar sight became a question that could be modelled. The accounts read here do not provide numbers of schools using the sphere, a commercial adoption register or savings attributed to the theory. We do not fill the everyday-life section with an invented merchant or farmer: the supported impact here is intellectual and experimental, with reception described within its evidence ^{19 14}.

Historical explanation does not require instructions for looking at the Sun or concentrating sunlight with glass. Symbols, a schematic and a contextual photograph can introduce the question. An old experiment's existence does not establish that repeating it is straightforward or safe for every child; understanding history is not a requirement to reenact every procedure.

The model moved investigation from a distant phenomenon difficult to isolate into an accessible analogue, large relative to a drop. The sources discuss this move together with the two internal paths, not as the invention of every experiment in history. Critical revision of a predecessor was part of the achievement, not a reason to erase that predecessor's contributions ²⁰.

It also permits a history without compulsory triumph. A useful path explanation and a failed colour theory can belong to the same author. Keeping both visible prevents modern answers from becoming concealed repairs to the past. Historical importance does not depend on every statement being correct or on an exclusive worldwide priority award ^{13 1}.

Sunni — declared frame: the individual's Islamic identity is documented; the museum's frame remains separate from priority adjudication. Academic account: MacTutor preserves Boyer's and Rashed's disagreement over the respective parts of al-Shirazi and al-Farisi. The museum reports those arguments through that source, without claiming to have compared every underlying original study ²¹.

The comparison with Theodoric means a similar problem was investigated elsewhere. Russell's absence of evidence for a Latin translation and the Science Museum's account of independent experiments are not a theft narrative. Nor should absence of one particular transmission document be made a philosophical proof that every conceivable route was absent ^{14 15}.

Teaching can distinguish three questions: where does light travel, how often does it reflect, and why do colours appear? The symbolic paths answer part of the first two. Counting their letters cannot derive all colours or intensities. This is a modern way to delimit the explanation, not a precision test conducted with al-Farisi's instrument.

The photograph is modern Alaska, not a chamber in Tabriz. It contains a valley, mountains, a conspicuous inner bow, a fainter higher bow and people, including a central red-jacketed figure. We do not infer experimental accuracy from an image without measurement parameters or turn its location into the invention's birthplace ²².

The actual readings here are MacTutor, Russell's article body in the browser, and the Science Museum article. The full Rashed paper could not be downloaded; only its opening was read, not the whole investigation. No original Tanqih manuscript or Hyderabad edition was inspected. Russell's bibliography warns of textual and diagram errors in that edition ²³.

Eric Rolph's photograph was inspected with its rights record: CC BY-SA2.5. Its upload date is not an established capture date. The unchanged original is used, not the variant with people removed. The Science Museum's photographs are not reused merely because its article can be read; those images have their own rights ²⁴.

A work called a revision can be more than repetition. Russell describes the distinction between the predecessor's voice and the reviser's, and the re-examination of conclusions. We paraphrase rather than replace explanation with long quotations. A book title alone establishes neither the validity of every proposition nor a lack of originality ³.

The museum article connects an observable rainbow with histories of explanation. Such a connection needs neither an invented legend nor a counterfeit historical picture. Today's photograph can remain today's photograph, with a clear boundary between a scholar's reported evidence and the museum's modern teaching language ²⁵.

On paper, imagine light entering a drop, reflecting once and leaving. Then imagine a second path with two reflections before exit. Comparing T-R-T with T-R-R-T helps separate boundary crossings from reflections. These are teaching symbols, not newly discovered manuscript letters or a drawing that fixes every angle.

Ask next whether a sphere explains everything. Glass matters, and counting reflections alone does not explain colour. Al-Farisi succeeded in some respects while retaining limits in others, as the sources explain. You can understand that question without looking at the Sun or performing a direct light-focusing experiment ^{26 1}.

• MacTutor: biography, experiment and attribution debate ²⁷.
• Russell, Encyclopaedia Iranica: structure, paths, colour and reception ²⁸.
• Science Museum: two bows and Theodoric comparison ²⁵.
• Commons: modern contextual photograph and rights ²⁴.