When a beam of light in air hits another transparent material, such as a slab
of glass or a pool of water, it changes direction. That鈥檚 refraction, the
phenomenon at the heart of most optical devices, including the human eye, and
which explains why a toothbrush standing in a glass of water looks broken.
The law of refraction, which applies to other types of waves besides light,
is named after Dutch astronomer Willebrord Snell, who is credited with its
discovery in 1621. Snell鈥檚 law is a tiny thing, with just half a dozen
mathematical symbols. It relates the angles of the beam before and after
refraction to a number鈥攖he refractive index-which is characteristic of the
material.
For nearly four centuries, Snell鈥檚 law has underpinned the design of all
things optical鈥攖elescopes, cameras, microscopes and so on. With a little
help from Snell, it鈥檚 possible to design materials to order, with refractive
indices specified beforehand. In California, researchers have even made a
material that bends microwaves the wrong way鈥攕omething not found in nature
and which opens up the possibility of new devices with weird properties.
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So Snell鈥檚 law is as powerful as ever. The only problem is its name: for
Willebrord Snell was not the first to discover it.
Just off the shore of North Carolina lies tiny Roanoke Island, the site of
the first English colony in America. Here, in 1585 a hundred settlers sent by
Sir Walter Raleigh set up home. For a year, they lived, built, explored, planted
and, lying in their huts at night, battled heat, mosquitoes and loneliness while
dreaming of the future.
One of these doughty men was Thomas Harriot, 鈥渕athematician and astronomer鈥�.
You might think this a strange occupation for a would-be settler in the New
World. So who was Harriot? Was he a real mathematician? Was he an astronomer or
just a common navigator? And what was he doing there on the shores of America?
Harriot was indeed a mathematician. He derived fundamental theorems in
cartography, trigonometry and algebra, and added the symbols > and < to the
mathematical lexicon. He worked on mirrors and lenses, and built telescopes at
the same time as Galileo. With these he independently discovered the phases
of Venus, made the first map of the Moon, and anticipated Galileo in observing
sunspots and measuring the periods of the satellites of Jupiter. His
observations of the comet of 1607, later to become famous as Halley's
comet, were good enough to be used in orbital calculations two hundred years
later. But all that lay in the future.
In 1585, Harriot was 25 years old, a graduate of the University of Oxford,
and employed by Raleigh as a teacher of mathematics, astronomy and navigation.
But it was not as a navigator that he travelled to America. By then that was the
captain鈥檚 routine job. Harriot鈥檚 chief tasks were to explore the land and study
the natives鈥� language. On his return he published A Briefe and True Report
of the New Found Land of Virginia, the first English treatise on the New
World. Among descriptions of native peoples, animals, plants and minerals, he
mentions tobacco, which later made Virginia wealthy. Harriot became a heavy
smoker and is credited with introducing clay pipes to England.
Among Harriot鈥檚 wide-ranging interests was the phenomenon of refraction. The
law of refraction was eagerly sought by designers of optical instruments as well
as astronomers keen to correct for the effect of the Earth鈥檚 atmosphere on
starlight. The inherited lists and rules of thumb for describing refraction were
known to be incomplete and, in places, wildly inaccurate.
Unlike the eminent German astronomer Johannes Kepler, who disdained
painstaking experimentation and relied instead on various approximate formulae
arrived at by speculation, Harriot perfected a simple technique for observing
refraction. He laid a thick, triangular pane of glass flat on a sheet of paper
and squinted along the table top, looking through the glass at a pin positioned
beyond it. By moving the pin around and comparing the positions of the pin and
its image, he was able to work out the directions of the incident and the
refracted rays, and measure their relationship. Like modern scientists, he was
not fully satisfied with his readings until they had been verified repeatedly by
friends and associates.
Based on his careful observations, Harriot had discovered the correct law of
refraction by 1602, 19 years before Snell. He used it to calculate the paths of
rays of sunlight entering a spherical drop of water, where they are reflected
off the rear surface before leaving the drop again. This calculation allowed him
to derive correctly the angular diameter of the rainbow鈥攁n ancient problem
of physics, whose solution was published in 1637 by Rene Descartes.
In 1606, Kepler heard of Harriot鈥檚 work, and promptly wrote to him asking for
information on refraction and the rainbow. Harriot replied, but was unwilling to
give away the fruits of his labour so easily, and excused himself on grounds of
ill health. But although he did not reveal the law of refraction or the size of
the rainbow, he did hint at something much deeper. Harriot was a follower of the
atomic doctrine of Democritus, and explained it to Kepler:
鈥淎 dense diaphanous body, therefore, which to the senses appears to be
continuous in all parts, is not actually continuous. But it has corporeal parts
which resist the rays, and incorporeal parts, vacua, which the rays penetrate.
So that refraction is nothing else than an internal reflection, and the part of
the rays which are received inside, although to the senses it appears straight,
is nevertheless composed of many straight line segments.鈥�
In this intuitive way, Harriot anticipated the modern atomic theory of
refraction, which treats light as a wave that is absorbed and re-radiated by
atoms, and propagates freely in the vacuum between them. Were it not for the
fact that he published very little and so remained virtually unknown, Harriot
would be celebrated as one of the founders of modern science.
The reasons Harriot kept so quiet during his life are complex. Politics
certainly played a role, for Raleigh was executed by King James I, and even
Harriot went to prison for a while. But overshadowing Harriot鈥檚 unfortunate
choice of patron was his stubborn belief in atoms. Atomism and the belief
in the indestructibility of atoms was regarded as a form of atheism because it
ran counter to the dogma of divine creation. Atheism was a treasonable offence
and Harriot鈥檚 work was investigated by the authorities. No charges were brought,
but the stigma remained.
Harriot鈥檚 thinking was centuries ahead of his time. The advice he offered
Kepler in response to his query about the rainbow could equally be given to a
young student setting out on a career in physics today: 鈥淚 have now conducted
you to the doors of nature鈥檚 abodes, where its mysteries lie hidden. If you
cannot enter, because the doors are too narrow, then abstract and contract
yourself mathematically to an atom and you will easily enter, and when you have
come out again, tell me what miraculous things you saw.鈥� Now that we know that
atoms exist, we can see that Harriot鈥檚 recommendation was spot on.