## The Speed of Light and the Index of Refraction

"Nothing can travel faster than the speed of light."
"Light always travels at the same speed."

Have you heard these statements before? They are often quoted as results of Einstein's theory of relativity. Unfortunately, these statements are somewhat misleading. Let's add a few words to them to clarify. "Nothing can travel faster than the speed of light in a vacuum." "Light in a vacuum always travels at the same speed."  Those additional three words in a vacuum are very important. A vacuum is a region with no matter in it. So a vacuum would not contain any dust particles (unlike a vacuum cleaner, which is generally full of dust particles).

Light traveling through anything other than a perfect vacuum will scatter off off whatever particles exist, as illustrated below.

In vacuum the speed of light is

 c = 2.99792458 x 108 m/s

This vacuum speed of light, c, is what the statements from relativity describe. Whenever light is in a vacuum, its speed has that exact value, no matter who measures it. Even if the vacuum is inside a box in a rocket traveling away from earth, both an astronaut in the rocket and a hypothetical observer on earth will measure the speed of light moving through that box to be exactly c. No one will measure a faster speed. Indeed, c is the ultimate speed limit of the universe.

That's not to say that nothing ever travels faster than light. As light travels through different materials, it scatters off of the molecules in the material and is slowed down. For some materials such as water, light will slow down more than electrons will. Thus an electron in water can travel faster than light in water. But nothing ever travels faster than c. The amount by which light slows in a given material is described by the index of refraction, n. The index of refraction of a material is defined by the speed of light in vacuum c divided by the speed of light through the material v:

n = c/v

The index of refraction of some common materials are given below.

 material n material n Vacuum 1 Crown Glass 1.52 Air 1.0003 Salt 1.54 Water 1.33 Asphalt 1.635 Ethyl Alcohol 1.36 Heavy Flint Glass 1.65 Fused Quartz 1.4585 Diamond 2.42 Whale Oil 1.460 Lead 2.6
Values of n come from the CRC Handbook of Chemistry and Physics

 The values of n depend somewhat on wavelength, but the dependence is not significant for most applications you will encounter in this course. Unless you are told otherwise, assume the index of refraction given you is appropriate for the wavelength of light you are considering.

Those materials with large indices of refraction are called optically dense media. (A medium is just a fancy word for a type of material.) Materials with indices of refraction closer to one are called optically rare media. Being naturally lazy creatures, we generally drop the word "optical'' and talk about dense and rare materials. Just be careful not to confuse dense and rare in the optical context with mass density!

Notice that the index of refraction of air differs from the index of refraction of vacuum by a very small amount. For applications with less than 5 digits of accuracy, the index of refraction of air is the same as that of vacuum, n= 1.000.  You will probably not encounter a situation in which the differenc between air and vacuum matters, unless you plan a future in precise optics experimentation.

Even though light slows down in matter, it still travels at an amazing speed, even through a dense material such as lead still travels at an amazing speed.  (Although light does not travel far through lead before being absorbed, high-energy gamma rays can travel a centimeter or so through lead at the speed calculated here.)  Using the definition of n, we can find the speed of light through lead:

vlead = c/nlead= (2.99792458 x 108  m/s) /(2.6) = 1.2 x 108 m/s = 2.6 x 108miles per hour

Even slowed by lead, light travels at a speed of 260 million miles per hour! That's more than 10,000 times the speed of the orbiting space shuttle. (According to a NASA site, the space shuttle travels 17,322 miles per hour when in orbit.)