An optical fiber has a core and a cladding. The core diameter of a single mode fiber is approximately 9 micrometers. But more than the geometrical core, the Mode field diameter is important for an optical fiber for transmission. Mode field diameter is the diameter of the light travelling area inside the fiber. It includes core and some portion of the cladding too.
The core and the cladding have different refractive indices. This means the light travels at different speeds at core and cladding. This difference is very low, but is very important for the optical fiber to carry the light along its length. Due to this refractive index difference between the core and cladding, the light hits at the border of the core will return back and hit at the opposite border and again reflect back. This process of total reflection is called Total Internal Reflection. Total Internal Reflection or TIR is the basic principle on which an optical fiber works.
Core has slightly higher refractive index than the cladding. The light theories says, when light travels from a medium of higher refractive index to a medium of lower refractive index, the light reflect back. This total internal reflection is shown in the diagram.
If n1 is the refractive index of core and n2 is the refractive index of cladding, then n1>n2 is the condition for total internal reflection.
Some back reference to the velocity of light here will be useful to remember. The speed of light in vacuum is 300,000 km per second. If light travels through a medium at a speed of 200,000 km per second, the refractive index of the medium is 1.5. The calculation is as simple as this. The refractive index is calculated by dividing the speed of light in vacuum by the speed of light in the medium.
So, to put in the form of mathematical formula; Refractive index of a medium = Speed of light in vacuum/Speed of light in the medium.
Total internal reflection happened and the light travelled all the way along the fiber carrying our valuable Voice, data, video and image. How useful is this total internal reflection!