A focus drawn on paper
At the Buyid court near the end of the tenth century, Ibn Sahl faced a problem that had to survive the trip from a diagram to a workshop. How should a piece of glass be shaped so that parallel sunlight passing through it would meet at one point?
Knowing that light bent inside glass was not enough. Rays crossing the center and the edge of a lens had to turn by exactly the right amounts. Otherwise the sharp focus on paper would become a pale blur in the craftsperson’s hands.
In his treatise On Burning Mirrors and Lenses, Ibn Sahl repeatedly drew rays, surfaces, and right triangles. The diagram below enlarges one small part of a lens surface and isolates the decisive crossing from air into glass.
Diagram description
Static physics diagram: Sunlight enters glass.
Changing the angle of incidence does not change the refracted angle by a fixed amount. Ibn Sahl’s geometrical ratio was equivalent to the sine relation later used as the law of refraction. A lens no longer had to emerge from trial and error alone. Its surface could first be determined on paper.
A law made to serve an object
The relation did not immediately enter European textbooks under Ibn Sahl’s name. Manuscripts disappeared, names changed, and knowledge did not travel along one straight road. Yet an important order of events had already appeared. A grand optical law did not come first and then find an application. The attempt to gather sunlight into one point forced the law out of a particular object.
A few decades later, Ibn al-Haytham would bring rays into a much wider program of experiment. He inherited more than Greek books. He entered an optical world that had already begun drawing, measuring, and doubting again.
Historical source: Encyclopaedia Iranica: Optics.