## Definition

Refraction occurs when light or other electromagnetic radiation passes between two media with different optical densities. In anything other than a complete vacuum, photons of light travelling through will sometimes collide with any molecules or sub-atomic particles that happen to be there. These collisions and the resulting extra distance for each photon causes light to travel at different speeds within different materials.

[SVG: Animation of light particles]

## Refractive Index

The ratio between the speed of light in a vacuum compared to the speed of light within a particular material is termed that material’s refractive index. This is a key concept when discussing refraction and the mathematical relationship is given as follows:

$$n = \frac {C_v} {C_m}$$

where:

• n is the refractive index of a material,
• Cv is the speed of light in a vacuum (2.99792458 x 108 m/s), and
• Cm is the apparent speed of light within that material (m/s),

Materials with a higher refractive index are typically denser than materials with a lower refractive index as they simply contain more stuff to collide with which slows the light down. It should also be noted that even opaque materials can have a refractive index, it is just that the light will not travel very far into the material before it is entirely absorbed.

## Units and Measures

The refractive index is a unit-less ratio. The refractive index of a vacuum is 1.0, which is the lowest possible value as nothing can theoretically travel faster than the speed of light in a vacuum. For all other materials it will be larger than 1.0. Air, for example, has a value of 1.000293, water is 1.333 and Diamond is 2.418. For a more detailed list, see the Example Values section below.

### Angle of Refraction

If the refractive index of a material and the angle of incidence of a beam of light is known, then the angle of refraction is given by Snell's Law, which is as follows.

$$\frac {n_1} {n_2} = \frac {\sin \theta_i} {\sin \theta_x }$$

This can be simply re-arranged to give the angle of refraction:

$$\theta_x = \sin^{-1} \left( \frac {n_2 \sin \theta_i} {n_1} \right)$$

where:

• n1 is the refractive index of the medium the light is travelling from,
• n2 is the refractive index of the medium the light is travelling into,
• θi is the angle of incidence, in degrees or radians, and
• θx is the angle of refraction, in degrees or radians.

The specification of degrees or radians means that it depends upon which maths library you are using and how it requires you to provide angle input for the sin and cos trigonometric functions. If you are using a pocket calculator, you can usually switch modes and enter either degrees or radians. If you are implementing these equations in computer code, you will very likely need to use radians.

## Example Values

The following are some representative refractive indices for various materials, gasses and liquids that I have collected over the years. I used to have solid web references for most of them, but those links have long since moved on or died, so probably best to treat these values as indicative. A great reference to check for accurate values is http://refractiveindex.info/.

Refractive Index:

Optics: