# Refraction

### Definition

Refraction is when a wave changes speed as it travels from one medium to another. If a ray of light hits a new medium at an angle to the normal, it will change direction.

#### Medium

A medium is a material which a wave can travel through.

An optical medium is a material which visible light can travel through, i.e. it is transparent or translucent.

### Refractive Index

The refractive index of an medium is the ratio of the speed of light in a vacuum to the speed of light in the medium. This concept can also be applied to other types of wave, such as sound, in which case a different reference medium other than a vacuum has to be used as sound cannot travel through a vacuum.

Different wavelengths diffract by different amounts - shorter wavelengths diffract more. An easy way to remember this is that Blue Bends Best. The refractive index can also be found using the ratio of the wavelengths before and after refraction.

The refractive index must be at least 1, as the speed of light in a medium cannot be greater than the speed of light in a vacuum, the theoretical maximum.

The refractive index of air is $1.0003$, which for Higher purposes is considered equal to the refractive index of a vacuum ($1$), as the difference is considered negligible.

#### Relative Refractive Index

A refractive index of a medium can also be calculated relative to a medium the wave enters from. This can be less than 1 and can be calculated for any kind of wave.

#### Formula

$n=\frac{{v}_{1}}{{v}_{2}}=\frac{\mathrm{sin}{\theta }_{1}}{\mathrm{sin}{\theta }_{2}}=\frac{{\lambda }_{1}}{{\lambda }_{2}}$
Variable Key
• $n$ is the refractive index of the medium.
• ${v}_{1}$ is the velocity of the wave in the source medium, or in a vacuum.
• ${v}_{2}$ is the velocity of the wave after entering the medium.
• ${\theta }_{1}$ is the angle from the wave to the normal in the faster medium (e.g. in a vacuum).
• ${\theta }_{2}$ is the angle from the wave to the normal in the slower medium
• ${\lambda }_{1}$ is the wavelenth of the wave in the source medium, or in a vacuum.
• ${\lambda }_{2}$ is the wavelength of the wave after entering the medium.

### Critical Angle

The critical angle is the angle at which an incident wave creates an angle of refraction perpendicular to the normal (i.e. an angle of refraction of ${90}^{\circ }$). This is the threshold at which total internal reflection can occur, as an angle of refraction greater than ${90}^{\circ }$ would prevent the wave from escaping its source medium. This can only occur when the wave is travelling from a slower medium towards a faster medium.

#### Formula

The critical angle of a medium can be calculated from the relative refractive index, and vice versa. Since $\mathrm{sin}{90}^{\circ }=1$, by substituting $\mathrm{sin}{\theta }_{1}$ we can get:

$n=\frac{1}{\mathrm{sin}{\theta }_{c}}$
Variable Key