That's a lotta' nice formulae you have there...but what does it mean ?
Snell's Law predicts the angle by which electromagnetic
radiation refracts when it passes from one material to
another. In order words, it predicts how light changes direction when it
passes through a lens, for instance.
The writeups above miss to inform you that the index of refraction for a
medium is the ratio of the speed of light in vacuum to the speed
of light in the medium. Air at freezing temperature (freezing water,
duh!) have n = 1.0003. Warmer air has higher n, and this is why
you may see strange mirror effects on hot asphalt roads in the summer; the air
has an abnormally high refractive index, and bends the light from cooler air.
This law was discovered in 1621 by Dutch scientist Willebrord van Roijen
Snell (Snellius), but was never published. Renée Descartes (Cartesius)
published this result in 1637 without quoting the source. Have you ever
heard about such rudeness ? Anyhow, Christiaan
Huygens mentioned the discovery made earlier by Snell in his work Traité de la lumière
(1690), where he introduces the concept of light as a wave. This results in
Snell receiving all due respect from colleagues and the public and all is
well, except in France where Snell's Law is called...yes Descarte's Law.
The story doesn't end here, though. All is well with Snell's Law through the centuries,
and it keeps on governing every little refraction in the world; glasses,
microscopes, radars etc.
In the latest issue of Science, scientists from the UCLA San Diego
reports to having created a material with a negative index of refraction.
This means that the material basically reverses the meaning of Snell's Law. When
tested with microwaves of similar frequencies being used in police
radars - hint, hint - the reflected microwaves went in the opposite
direction of that predicted by Snell's Law. Now, if we only could figure out
a use for this outside of the laboratories...
The material is a composite of fiberglass and copper wires, so it does
not work on optical frequencies i.e. light. The military is of course
looking into what applications - other than speeding - that can come out of
Reference: ne.se, britannica, Scientific American