** Next:** Dispersion
**Up:** Wave Properties of Light
** Previous:** Reflection

**Refraction** is the bending of light as it passes
between materials of different optical density.

**Definition:** Index of Refraction

**Index of Refraction** of
a material is the
ratio of the speed of light in vacuum to the speed of light in that
material:

n =
| (1) |

**Note: **

- The more dense the material, the slower the speed of light in that
material. Thus
*n*> 1 for all materials, and increases with increasing density.*n*= 1 in vacuum. - The frequency of light does not change when it passes from
one medium to another. According to the formula
*v*=*f*, the wavelength must change. The index of refraction can therefore be written in terms of wavelengths as:*n*=(2)

**Idea: **Explanation for Refraction of Light

The change in speed and wavelength at the boundary between two materials causes light to change direction. Think of a car approaching a patch of mud at a sharp angle from a well paved road. The tire that hits the mud first will slow down, while the other tire is still going fast on the good road. This will cause the car to turn, until both tires are in the mud and going at the same speed. If is the angle of the ray relative to the normal to the surface in medium 1, and is the angle relative to the normal in medium 2, then:

= = = | (3) |

**Note: **

- This relationship between the angles is called
**Snell's Law**. - The relation between the two angles is the same whether the ray is moving from medium 1 to 2 (so that is the angle of incidence and is the angle of refraction) or whether the ray moves from medium 2 to medium 1, so that is the angle of incidence and is the angle of refraction.

For a light ray passing from a more dense to a less
dense material,
there is a critical angle of incidence for which the
angle of
refraction is 90^{ o }. For greater angles of incidence, the
light cannot pass through the boundary between the materials, and
is reflected within the more
dense material. For a light ray trying to pass from medium 2 to
medium 1, the critical angle is given by:

sin = sin 90^{ o } =

10/9/1997