section_path: Classical optics/Geometrical optics/Refractions
section_name: Refractions
paragraph_text: Refractions
  
  Refraction occurs when light travels through an area of space that has a changing index of refraction; this principle allows for lenses and the focusing of light. The simplest case of refraction occurs when there is an interface between a uniform medium with index of refraction n and another medium with index of refraction n. In such situations, Snell's Law describes the resulting deflection of the light ray:
  
  n 1 sin θ 1 = n 2 sin θ 2 {\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}}
  
  where θ and θ are the angles between the normal (to the interface) and the incident and refracted waves, respectively.
  
  The index of refraction of a medium is related to the speed, v, of light in that medium by n = c / v, {\displaystyle n=c/v,} where c is the speed of light in vacuum.
  
  Snell's Law can be used to predict the deflection of light rays as they pass through linear media as long as the indexes of refraction and the geometry of the media are known. For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism. In most materials, the index of refraction varies with the frequency of the light, known as dispersion. Taking this into account, Snell's Law can be used to predict how a prism will disperse light into a spectrum. The discovery of this phenomenon when passing light through a prism is famously attributed to Isaac Newton.
  
  Some media have an index of refraction which varies gradually with position and, therefore, light rays in the medium are curved. This effect is responsible for mirages seen on hot days: a change in index of refraction air with height causes light rays to bend, creating the appearance of specular reflections in the distance (as if on the surface of a pool of water). Optical materials with varying indexes of refraction are called gradient-index (GRIN) materials. Such materials are used to make gradient-index optics.
  
  For light rays travelling from a material with a high index of refraction to a material with a low index of refraction, Snell's law predicts that there is no θ when θ is large. In this case, no transmission occurs; all the light is reflected. This phenomenon is called total internal reflection and allows for fibre optics technology. As light travels down an optical fibre, it undergoes total internal reflection allowing for essentially no light to be lost over the length of the cable.