Refraction
![[url=https://pixabay.com/en/diamond-brilliant-gem-jewel-shiny-1186139/]"Diamond"[/url] by ColiN00B is in the [url=http://creativecommons.org/publicdomain/zero/1.0/]Public Domain, CC0[/url]
The way light bends as it enters a diamond, as well as the conditions required for it to reflect internally, depend on diamond's refractive index - the topic of this section.](https://www.geogebra.org/resource/UhtjRF4g/CWXzl8lhLmAtRMYM/material-UhtjRF4g.png)
The last chapter focused primarily on light reflecting off of surfaces. In this chapter we will focus on how light bends when it passes through various transparent media like water or glass. The technical terms for this bending is refraction.
The extent to which light refracts as it passes from one medium to another depends on the variation in the speed of light in the different materials in question. If there is no change in speed, there will be no refraction.
If you are under the impression that the speed of light doesn't change, you are mistaken. The number that is referred to as the speed of light sometimes is really the speed of light in vacuum. That is a universal constant and is the fastest speed at which any entity can travel in our universe. The value of the speed of light in vacuum is . It is not exactly 3.0, but is very close.
When light passes through transparent media besides vacuum - things like air, glass, water, alcohol, diamond - it travels slower than in vacuum. The extent to which it slows is quantified by the refractive index or index of refraction of a medium. The refractive index is denoted . By definition .
| Material | Refractive Index |
| vacuum | 1 |
| air | 1.00028 |
| water | 1.333 |
| glass (avg) | 1.5 |
| diamond | 2.42 |
| ethanol | 1.36 |
| ice | 1.31 |
| table salt | 1.54 |
I'm sure you see that some values in that table are more precise than others. It turns out that the refractive index of a material will depend on the wavelength of the light used, so that too much precision isn't really justifiable since the wavelength isn't being specified. In practice what we'd want is a table of refractive index vs wavelength like the one for water below. We will see later in the chapter that the consequence of the wavelength-dependent refractive index is among other things, a rainbow. This dependence is called dispersion.
![CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=647022
The refractive index of BK7 glass (and other materials) depends on the wavelength of the light. Note that 0.8[math]\mu m[/math] is 800nm.](https://www.geogebra.org/resource/JuvVeTqp/xXG2SykFdD8A2JZj/material-JuvVeTqp.png)
The Speed of Light in Materials
As mentioned, the speed of light in vaccum is a universal constant. In all other media light travels slower than in vacuum. The speed in other media is given by In water, for instance, the speed of light is So light only travels 3/4 as fast through water as through the vacuum of space. This has implications about the path light will follow as it enters water. One implication is that water always looks shallower than it is. How much shallower does it appear? It appears 3/4 as deep as its actual depth, or shallower by a factor of the refractive index of water. While this connection may not be obvious we will discuss the proof using the small angle approximation in class.
AN ASIDE: This discussion might make you wonder about something. I remember wondering about it as a student. You might have heard before that the speed of light in vacuum is the absolute speed limit in our universe. That being true, you might wonder if anything can travel faster than light in other media besides vacuum. The answer is yes.
While nothing can outrun (or even match) the speed of light in vacuum, sometimes material particles will outrun light in other media. While it happens both in nature and in laboratory settings, the outcome is interesting for charged particles. I should first say that neutral particles can do so without any significant consequences. For charged particles outrunning light in non-vacuum, nature quickly puts a stop to it by the object bleeding off energy in the form of high energy radiation - the most common variant of which is called Cherenkov radiation. This radiation will reduce the energy of the moving object and will only cease when the object's speed is below v=c/n for the medium. This is the equivalent of an electromagnetic shock wave - like the sonic shock waves that supersonic jets produce in air when they go faster than sound does through air.
What About Other Properites of Light?
Light has a wavelength and a frequency. It is appropriate that we discuss what happens to them inside media other than vacuum. The result is that the frequency never changes. The wavelength is shortened by a factor of the refractive index n. So it turns out that the equation for waves in general, which relates wave speed , wavelength and frequency , is valid in both vacuum and in any other medium: .