10.11 Refraction  (Page 2/5)

The speed of light is now known to great precision. In fact, the speed of light in a vacuum $c$ is so important that it is accepted as one of the basic physical quantities and has the fixed value

where the approximate value of $3\text{.}\text{00}\times {\text{10}}^8\text{m/s}$ is used whenever three-digit accuracy is sufficient. The speed of light through matter is less than it is in a vacuum, because light interacts with atoms in a material. The speed of light depends strongly on the type of material, since its interaction with different atoms, crystal lattices, and other substructures varies. We define the index of refraction     $n$ of a material to be

where $v$ is the observed speed of light in the material. Since the speed of light is always less than $c$ in matter and equals $c$ only in a vacuum, the index of refraction is always greater than or equal to one.

That is, $n\ge 1$ . [link] gives the indices of refraction for some representative substances. The values are listed for a particular wavelength of light, because they vary slightly with wavelength. (This can have important effects, such as colors produced by a prism.) Note that for gases, $n$ is close to 1.0. This seems reasonable, since atoms in gases are widely separated and light travels at $c$ in the vacuum between atoms. It is common to take $n=1$ for gases unless great precision is needed. Although the speed of light $v$ in a medium varies considerably from its value $c$ in a vacuum, it is still a large speed.

Law of refraction

[link] shows how a ray of light changes direction when it passes from one medium to another. As before, the angles are measured relative to a perpendicular to the surface at the point where the light ray crosses it. (Some of the incident light will be reflected from the surface, but for now we will concentrate on the light that is transmitted.) The change in direction of the light ray depends on how the speed of light changes. The change in the speed of light is related to the indices of refraction of the media involved. In the situations shown in [link] , medium 2 has a greater index of refraction than medium 1. This means that the speed of light is less in medium 2 than in medium 1. Note that as shown in [link] (a), the direction of the ray moves closer to the perpendicular when it slows down. Conversely, as shown in [link] (b), the direction of the ray moves away from the perpendicular when it speeds up. The path is exactly reversible. In both cases, you can imagine what happens by thinking about pushing a lawn mower from a footpath onto grass, and vice versa. Going from the footpath to grass, the front wheels are slowed and pulled to the side as shown. This is the same change in direction as for light when it goes from a fast medium to a slow one. When going from the grass to the footpath, the front wheels can move faster and the mower changes direction as shown. This, too, is the same change in direction as for light going from slow to fast.