Treatise on Light

Overview

The Treatise on Light is a hundred and twenty-eight pages in six chapters, written in French and published at Leiden in 1690, though Huygens had presented the substance of it to the Paris Academy in 1678. He apologises in the preface for the delay and for the state of the prose, which he says he never polished.

Christiaan Huygens was Dutch, the son of a diplomat and poet, and possibly the best physicist of the generation between Galileo and Newton. He discovered Titan and worked out the shape of Saturn’s rings, invented the pendulum clock and the balance spring, wrote the first treatise on probability, and here produced the wave theory of light.

The book’s reputation is bound up with its defeat. Newton’s Opticks appeared fourteen years later, argued for light as a stream of corpuscles, and carried the field on the strength of its author’s standing and the difficulty the wave theory had explaining why light travels in straight lines rather than spreading round corners like sound. Huygens’ account lay largely unused until Thomas Young’s interference experiments around 1801 and Fresnel’s work in the 1810s and 1820s.

He also knew what kind of argument he was making. The preface distinguishes his demonstrations from geometrical ones and says that his principles are verified by what follows from them and agrees with experience, which is a clear statement of hypothetico-deductive method eighty years before anyone had a name for it.

The argument

Chapter I: light as a wave. Huygens begins from something Rømer had established in 1676, that light has a finite speed, determined from the eclipses of Jupiter’s moons. If light takes time to travel, something must be travelling, and Huygens argues it cannot be matter, because beams cross without disturbing each other, and because light passes through glass and through the space above the atmosphere.

His model is sound. A disturbance spreads through a medium without the medium moving along with it. The medium for light he takes to be an ether of extremely small, hard, elastic particles filling all space and penetrating transparent bodies.

Then the construction. A wave from a luminous point reaches a surface. Every point of that surface becomes, in turn, the centre of a new spherical wavelet. The individual wavelets are too weak to be seen on their own, but where they all touch a common surface, their common tangent, the disturbance is reinforced, and that tangent is the wavefront an instant later. Propagate that forward and you have light travelling in straight lines, since the tangent surface advances and the sideways portions of the wavelets cancel.

This is a genuinely powerful idea and it is the whole book. It accounts for a wave that spreads spherically and nevertheless has a definite front.

Chapter II: reflection. The law of reflection derived from the construction, by drawing the wavelets generated as a plane wave meets a mirror, and finding that the tangent to them makes the angle of reflection equal to the angle of incidence.

Chapter III: refraction. The best chapter, and the one with the falsifiable prediction. Huygens supposes that light travels more slowly in a dense medium than in air, because the ether particles inside matter are less free to move. Apply the wavelet construction across the boundary with the wavelets in the second medium smaller, since they spread less far in the same time, and the resulting tangent is tilted: the ray bends toward the normal. The ratio of the sines comes out exactly as Snell’s law requires, and it equals the ratio of the speeds.

The consequence is that light must go slower in water than in air. Newton’s corpuscular theory needed the opposite, an attraction at the surface accelerating the particles into the denser medium. Neither side could measure it. Foucault did, in 1850, and found Huygens right.

Chapters IV and V: Iceland spar. The longest and most impressive section. A crystal of Iceland spar, calcite, placed on a page, shows every letter twice. One image behaves normally; the other refracts in a way that violates Snell’s law, shifts when the crystal is rotated, and does not vanish at normal incidence.

Huygens works at this for two chapters, measures carefully, and produces an account: the ordinary ray propagates by spherical wavelets, as in glass, and the extraordinary ray by spheroidal ones, ellipsoids of revolution aligned with the crystal’s axis. Apply the same tangent construction to both and the observed geometry falls out correctly.

He then notices something he cannot explain. Take a ray that has passed through one crystal and send it through a second: whether it splits again depends on the orientation of the second crystal relative to the first. The light has acquired a property by passing through the first crystal, a sidedness. Huygens describes the effect precisely, says frankly that he has not been able to account for it, and leaves it. It is polarisation, and explaining it required treating light as a transverse rather than a longitudinal wave, which is what Fresnel did a hundred and thirty years later.

Chapter VI: the cause of transparency and opacity, and some final remarks on the ether.

How to read it

Read the preface and chapter I with a pencil, and draw the wavelet construction yourself. It is the whole book in two diagrams and it is genuinely beautiful once you have drawn it.

Then chapter III for refraction and the speed prediction, which is the theory’s most testable consequence and the place where it beat its rival.

Chapters IV and V are harder and worth attempting for one thing: watching a first-rate scientist get an unfamiliar phenomenon geometrically right while candidly admitting that a related effect defeats him.

Use the Thompson translation, which is free and complete, and be ready for the diagrams to do most of the work.

Read it against Newton’s Opticks. The two books are close in date, disagree fundamentally, are both excellent, and the disagreement was not settled by argument. That is worth sitting with.

And keep the ether in view. Huygens’ theory requires a material medium filling all space, and that requirement outlived his other claims and was only abandoned after Michelson and Morley failed to detect it in 1887. The part of his theory that was wrong survived longest.

Questions it raises

• The wavelet construction works and Huygens gives no reason why the backward-travelling wavelets should cancel. Does a construction that predicts correctly need a justification?
• He says his principles are verified by their consequences rather than proved in advance. Is that a weaker kind of science or simply an honest description of most of it?
• The wave theory required light to slow in glass and the particle theory required it to speed up. Why did it take a hundred and sixty years for anyone to measure it?
• Huygens describes polarisation exactly and cannot explain it. What is the value of a precisely recorded anomaly?
• Newton’s authority carried the field. How much should the standing of a scientist weigh against an argument?
• The ether was the part of the theory that was wrong and the part that lasted longest. Why are background assumptions harder to dislodge than explicit claims?