Refraction in geometric optics:
The phenomenon of refraction takes place when a ray of light passes through a medium that has a changing index of refraction; this phenomenon allows for lenses and the focusing of the light. The simplest way to observe the refraction phenomena is when there is an interface between two mediums where the refractive index of the first medium is n1 and the refractive index of the second medium is n2 and when the ray of light passes through one medium to another it gets slightly bend. In such cases, Snell’s law is used to describe the slight deflection in the ray of light:
where Θ1 and Θ2 represent the angle between the normal and the incident and refracted rays.
The refractive index of a particular medium can be described as the:
where n represents the Refractive index, c represents the speed of light in a vacuum (i.e, 3×108 m/s) and v is the speed of light in that medium.
Snell’s law allows us to calculate how much the light will get deflected when it will pass through a linear media as long as the refractive indexes of both the mediums and geometry of both the mediums are known. For example, in the case of a prism when a ray of light travels through a glass prism the deflection that happens in the light depends upon the orientation and shape of the prism. In the majority of the mediums, the refractive index keeps on changing with the frequency of light. If we consider all this, then we can use Snell’s law to find out how a prism will disperse a ray of light in order to form a spectrum. The credit of the discovery of the phenomena of passing light through a prism goes to Isaac Newton. The process of optical prism manufacturing is performed in order to manufacture precision optics and custom optical lenses.
In the case of many mediums, their refractive index gradually changes with position and therefore light rays in that medium are curved. This effect is responsible for the mirages seen on hot days: changes in the index of refraction air with altitude bend the light rays, giving the appearance of specular reflections in the distance (as on the surface of a pool of water). The optical materials in which the refractive index keeps on changing are known as gradient-index (GRIN) materials.
Snell’s law predicts that if the value of Θ1 is very much larger than Θ2, then we neglect the value of Θ2.