# Treatise on Light

For Ibn al-Haytham's Treatise on Light, see Ibn al-Haytham#Optical treatises.
Author Christiaan Huygens French Optics 1690

Treatise on Light: In Which Are Explained The Causes of That Which Occurs in Reflection & Refraction (French: Traité de la Lumière: Où font expliquées Les causes de ce qui luy arrive Dans la Reflexion & Dans la Refraction) is a book written by Dutch polymath Christiaan Huygens that was published in French in 1690. The book describes Huygens' conception of the nature of light which makes it possible to explain the laws of geometrical optics as shown in Descartes' Dioptrique, which Huygens aimed to replace.[1]

Unlike Newton's rival corpuscular theory, which was presented in the Opticks,[2] Huygens conceived of light as an irregular series of shock waves which proceeds with very great, but finite, velocity through the ether, similar to sound waves. Moreover, he proposed that each point of a wave front is itself the origin of a secondary spherical wave, a principle known today as the Huygens-Fresnel principle.[3] The book is considered a pioneering work of theoretical and mathematical physics and the first mechanistic account of an unobservable physical phenomenon.[4][5]

## Overview

Huygens' ideas on light originated in his unpublished work on the properties of lenses and their configurations entitled Dioptrica, which began in 1652. In 1672, the problem of the strange refraction of the Iceland Crystal created a puzzle regarding the physics of refraction that Huygens wanted to solve.[6] Huygens eventually was able to solve this problem by means of elliptical waves in 1677 and confirmed his theory by experiments only after critical reactions in 1679.[7]

His explanation was based on three hypotheses: (1) There are inside the crystal two media in which light waves proceed, (2) one medium behaves as ordinary ether and carries the normally refracted ray, and (3) the velocity of the waves in the other medium is dependent on direction, so that the waves do not expand in spherical form, but rather as ellipsoids of revolution; this second medium carries the abnormally refracted ray. By studying the symmetry of the crystal, Huygens was able to determine the direction of the axis of the ellipsoids, and from the refraction properties of the abnormal ray he established the proportion between the axes. He calculated the refraction of rays on plane sections of the crystal other than the natural crystal sides, and ultimately verified all his results experimentally.[3][8]

Huygens intended to publish his results as part of the Dioptrica, but decided to separate his theory from the rest of the work at the last minute, marking the transition from geometrical optics to physical optics.[9]

## Propagation Medium

Origin of light waves as shown in Treatise on Light

In the first chapter, Huygens describes light as a disturbance which moves in a material medium of an unknown nature which he calls ethereal and which is different from that which propagates sound. This ethereal matter is composed of elastic particles of matter which collide according to laws he discovered in 1669. In the third chapter, On Refraction, he questions the way in which light spreads in liquids and transparent solids. In the former there is no problem in conceiving that particles in the liquid can move and transmit light disturbance.

However, the propagation of light in solids like glass or translucent minerals are not so easily explained. He considers that the structure of solid matter is atomic: "this solidity is not as it seems to us, being probable that these bodies are rather composed of particles which are only placed next to each other [... ] because their rarity [their low density] appears by the ease with which the matter of the vortices of the magnet passes through them, or that which causes gravity [...] It remains therefore that it is, as it was said, assemblies of particles which touch each other without composing a continuous solid."[10] The light waves can therefore move from one particle to another without these being displaced.

A second way of looking at the problem of the penetration of light into solids or liquids is to consider that it is not the particles of the transparent medium which transmit light but the particles of ethereal matter which permeate the interstices of the solid or liquid matter, or even a vacuum since light passes through the vacuum created at the top of Torricelli's barometer: “The rarity of transparent bodies being therefore such as we have said, it is easy to imagine that the waves can be continued in the ethereal matter which fills the interstices of the particles."[10] Finally, Huygens considers a third type of spread that would be a combination of the first two.

## Speed of Light

Huygens takes up the temporal conception of Pierre de Fermat. He considers that the "shaking" producing light waves necessarily moves at finite speed, even if it is very high. This point is very important because its demonstrations are based on the equivalence of travel times on different paths.[6][7]

He reports that Danish astronomer Ole Christensen Rømer told him that the speed of light is at least 100,000 times faster than the speed of sound, and possibly six times higher. In the latter case, the speed found by Rømer (214,000 km /s) was of the same order of magnitude as the speed of light admitted today.[5]

## Legacy

Wave refraction in the manner of Huygens

Huygens' Treatise on Light provides a qualitative explanation of the propagation of spherical and plane waves, and derives the laws of reflection and refraction from them. Although the completeness of Huygens' analysis is impressive, he was unable to comprehend the effect that we now recognize as polarization, which occurs if the refracted ray is directed through a second crystal of which the orientation is varied. He also did not address a number of issues, such as chromatic aberration and color, both of which were explained by Newton, although he had experienced them while building his telescopes.[3]

Huygens' ideas will be taken up and developed independently by Augustin-Jean Fresnel in his Mémoire sur la Diffraction de la Lumière (1818) to explain the interference and diffraction of light, leading to the Huygens-Fresnel Principle.[1][5]