# Archimedes to Hawking: Laws of Science and the Great Minds behind Them

By Clifford A. Pickover | Go to book overview

SNELL’S LAW OF REFRACTION

Netherlands, 1621. The angle of refraction of light that travels between two media depends on the refractive indices of the media and is described quantitatively by Snell’s Law.

CROSS REFERENCE: JOHANNES KEPLER AND MAXWELL’S EQUATIONS.

During the year that Snell discovered his law, the English
attempted to colonize Nova Scotia and Newfoundland, and pota-
toes were planted for the first time in Germany. The Mayflower
sailed from Plymouth colony in North America on a return trip
to England.

Light traveling through air bends, or refracts, when it passes into another material such as glass. When waves such as light waves are refracted, they experience a change in the direction of propagation due to a change in their velocities. Refraction typically occurs when a ray of light passes from one medium to another, and every known material slows light relative to its speed in a vacuum. In particular, the refraction of light occurs at the boundary between the media (e.g., between air and water), at which point the phase velocity of the wave changes, and the light changes direction of travel. Additionally, the wavelength of light changes at the interface between media, but the frequency of the light remains constant.

To understand the concept of phase velocity, imagine a sinusoidal wave made of a piece of wood and sliding to the right. The phase velocity is simply the ordinary speed with which the wooden wave is moving. Now imagine a wave in a pond, in which a leaf on the surface is oscillating vertically as the wave passes. In this case, the wave pattern moves to the right with phase velocity vp, just as with the wooden wave, but the leaf may have no lateral motion at all.

I like to demonstrate refraction to young people by placing my finger into my aquarium filled with large fish. Because air has a refractive index of 1.0003, and water has a refractive index of 1.33, when my guests look at my straight finger that is partially submerged in the water, the finger appears to bend abruptly at the surface of the water. Before the fish bite my finger, I explain to my guests that this apparent bending is due to the bending of light rays as they move from the water to the air. I then scribble Snell’s Law on a napkin,

-65-

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