Huygens: Treatise on Light

Christiaan Huygens (say HOY-gens) lived in the Netherlands and was good at almost everything. He built the first accurate pendulum clock, ground his own telescope lenses, and was the first to see that Saturn has a ring around it.

He wondered: what is light? He thought light might be like the ripples you see when you drop a stone into a pond. The ripples spread out in circles. Nothing flies across the pond; the water just jiggles and passes the jiggle along. Huygens thought light spreads the same way, through a fine invisible stuff that fills space.

Then he had a clever idea. Every spot that a wave reaches starts its own little ripple. All those little ripples together make the next wave. When light goes from air into water, the little ripples in the water grow more slowly, because light is slower there. So the wave tips and changes direction. That is why a straw in a glass of water looks bent!

Who, when and the problem

Christiaan Huygens (1629–1695) was born in The Hague, the son of the poet and diplomat Constantijn Huygens. By 1660 he was famous: he had found Saturn's moon Titan (1655), explained Saturn's ring (1659), built the first pendulum clock (1656) and written the first printed book on probability (1657). In 1666 he became a leading member of the new Royal Academy of Sciences in Paris. He presented his Treatise on Light to the Academy in 1679 and published it in French in 1690. Silvanus P. Thompson translated it into English in 1912.

The problem: what is light, and why does it reflect and bend as it does? The law of refraction (the ratio of the sines is fixed) had been found by Willebrord Snell around 1621 and published by Descartes in 1637, but Descartes's explanation needed light to be faster in glass. And in 1669 Erasmus Bartholin had described a strange crystal from Iceland that splits one ray into two, a puzzle no one could explain.

The main ideas

• Light is a motion, not a flying substance. Because beams of light cross each other without bumping, Huygens argued that light is a disturbance passed from particle to particle of a very fine matter, the ether, as sound is passed through the air.
• Light takes time to travel. Using Ole Rømer's 1676 timing of the eclipses of Jupiter's moon Io, he worked out how fast light goes.
• Every point of a wave is a source of new waves (Huygens's principle). The new wave front is the surface that touches all the little "particular" waves.
• Reflection and refraction follow. With this one idea he derived the law of reflection and the law of refraction, with the sine ratio equal to the ratio of the speeds. Light must go slower in water and glass.
• Double refraction. In Iceland crystal, he proposed, one ray makes spherical waves and the other makes waves shaped like squashed spheres (spheroids), because the crystal passes the motion faster in some directions. This explained the strange second ray.

The speed of light

Rømer noticed that the eclipses of Io come late when the Earth is far from Jupiter and early when it is near, as if the news of each eclipse took time to cross the Earth's orbit. Huygens took Rømer's figure of 22 minutes to cross the orbit and an orbit about 22,000 Earth diameters across, and found that light covers about 16⅔ Earth diameters every second.

Wavelets

Setting the record straight

• Huygens's waves were not quite our waves. He pictured light as a series of separate pulses with no regular rhythm. He had no idea of wavelength, which is why his theory could not explain colors, or the bright and dark fringes we now call interference. Thomas Young (1801) and Augustin Fresnel (1818) added those, and the idea is now called the Huygens–Fresnel principle.
• Who measured the speed of light? Rømer showed in 1676 that light takes time, and his work convinced many, but Huygens's treatise is one of the first places a numerical speed was worked out from it.
• Newton against Huygens. A common story says Newton's authority buried the wave theory for a century. Newton's particle view did dominate in Britain, but the wave theory also lacked an explanation of color and of why light casts sharp shadows, which Huygens could not fully answer.

What later science kept, and what it changed

• Kept: Huygens's principle is still the standard way to work out how waves bend, spread and diffract, for light, sound, water and radio. His prediction that light is slower in water was confirmed by Léon Foucault in 1850, against the particle theory's prediction.
• Changed: the ether. After Michelson and Morley (1887) failed to detect the Earth's motion through it, and Einstein's relativity (1905) did without it, light came to be understood as an electromagnetic wave that needs no medium, as Maxwell had found in the 1860s.
• Explained at last: the second ray in Iceland crystal comes from polarization, named by Étienne-Louis Malus in 1808. Huygens himself noticed the strange way two crystals act on light together and wrote plainly that he could not explain it.

A mechanical philosophy. Huygens believed that every explanation in physics must be in terms of matter in motion. That is why he rejected Newton's attraction at a distance, which seemed to him an "occult quality." His Discourse on the Cause of Gravity, printed with the Treatise on Light in 1690, tried to explain gravity by swirling ether. Compare Newton's "I frame no hypotheses": two great scientists with different ideas of what counts as an explanation.

Certainty in physics. In his preface Huygens says that in physics we cannot have the certainty of geometry. Instead, when a few principles explain many facts, and especially when they predict new ones that experiment then confirms, we may reach a very high degree of likelihood. This is close to how scientists talk about evidence today.

Huygens's other work. His Horologium Oscillatorium (1673) on the pendulum clock showed that a pendulum swinging along a cycloid keeps exactly equal time, and worked out the outward pull on a body moving in a circle, $v^2/r$, which Newton used in the Principia. His pendulum clocks made timekeeping about 60 times more accurate.