Ibn Sahl

Abū Saʿd al-ʿAlāʾ ibn Sahl, described by Roshdi Rashed as "the first mathematician known to study lenses" was a hugely influential figure, whose application of the law of refraction around 600 years before Snellius (for whom the law of refraction is named) gives us a remarkable insight into the scientific tradition of early Islam.

Biography

Unlike the other thinkers discussed on this website, not much is known about Ibn Sahl's life. Born around the year 940CE, Abū Saʿd al-ʿAlāʾ ibn Sahl was an earlier pioneer in the world of optics. He is the first known Muslim to have studied Ptolemy's 'Optics', and would inspire the work of Ibn Al-Haytham. Associated with the Buyids in Baghdad, but likely of Persian descent, he would go on to publish his crowning work "On the Burning Instruments" around 984CE. He died around the year 1000CE, and was often overshadowed by his contemporaries. However, he left a lasting legacy on the field of optics, and was a very early researcher into the geometry of lenses, and should be rightfully credited with the discovery of the law of refraction, often called Snell's law despite his independent discovery of the law over 600 years after the death of Ibn Sahl.

"On The Burning Instruments"

"On the Burning Instruments" was a manuscript describing the production and optics behind different types of lenses, including 2 kinds of burning reflectors (parabolic and ellipsoidal) and two types of lens (plano-convex and biconvex) for which there are diagrams below. This work, whilst an impressive display of the geometry of the Islamic golden age, is particularly significant because of one specific thing, the law of refraction.

Biconvex Lens

Has the same radius of curvature on both sides, focuses light to a point

Plano-Convex Lens

Has one flat edge and one curved edge, also focuses light to a point

Parabolic Reflector

Is a parabolic shape, reflects incoming light to a focus.

Ellipsoidal Reflector

Is an elliptical shape, reflects incoming light from a focus to a focus.

For Mathematical descriptions see the further reading page for Roshdi Rashed’s work.

The Law of Refraction

The law of refraction describes the relationship between the angle at which light is refracted and the density of the mediums through which it is traveling. In mathematical terms, the law of refraction is that n₁sin(θ₁)=n₂sin(θ₂), where θ₁ is the angle between the normal(perpendicular to the boundary) and the ray of light incident on a boundary, θ₂ is the angle following incidence between the ray and the normal, and the n values are the refractive indexes (a measure of how much light refracts when moving to that material from air) of the materials. This can be seen much better in the diagram besides the text.

"The first clear evidence we have of a correct understanding of Ptolemy's theory of refraction does not appear in the Arabic sources available to us until the second half of the tenth century, when the Persian mathematician al-Ala ibn Sahl was able to put Ptolemy's ideas to use in formulating entirely original geometrical arguments for the construction of burning instruments by means of refraction"
(Enterprise of Science in Islam: A New Perspective, J. P. Hogendijk,A. I. Sabra)

Ibn Sahl's use of refraction

Ibn Sahl wasn't the first person to notice the relationship between a medium and its angle of refraction, that was Ptolemy in his book 'Optics'. However, Ibn Sahl seems the first person to use the law mathematically, using it to construct and produce the lens' described above, and to do so geometrically, without any aberration(distortion). The above image shows a reproduction of his diagram showing the law of refraction, one he would use throughout his books to construct lens' with which he experimented.

Despite this clear discovery of the law, it would go on to be named "Snell's Law" in much of Europe and the Americas, after Willebrord Snellius, who rediscovered it in the 17th century.

Ibn Sahl has been clearly lost by scientists, substituted with north-western scientific canon. Whilst it does seem that Descartes and Snellius were not familiar with Ibn Sahl's work, we have, I think, unfairly attributed this law to the two of them, as opposed to the man who first came up with the correct ratios. It is important to note that the text on the burning instruments is still only recently rediscovered, around 30 years ago. Whilst any wide sweeping changes in that time are unlikely, the change should come, in the interest of correct accreditation.