Waves and Light: Refractive Index

Key Concepts in Refractive Index

Refractive Index, denoted as ‘n’, is a measure of how much the speed of light is reduced within a given medium compared to its speed in a vacuum.
It is a dimensionless quantity, calculated as the ratio of the speed of light in a vacuum, ‘c’, to the speed of light in the medium, ‘v’.
Therefore, the formula for refractive index is given as n = c/v.
A higher refractive index indicates a greater reduction in the speed of light within the medium, implicating a denser medium.
Refractive index also indicates how much a wave is refracted, or bent, when it enters that material from another medium.

Total Internal Reflection is a phenomenon that occurs when a wave travelling in a medium hits the medium boundary at an angle greater than a certain critical angle, causing the wave to be completely reflected within the medium.
The critical angle is the angle of incidence beyond which rays of light passing through a denser medium into a less dense medium are no longer refracted but totally internally reflected.
The critical angle can be calculated using the formula: sin(critical angle) = n2/n1, where n1 is the refractive index of the denser medium and n2 is the refractive index of the less dense medium.

Snell’s Law quantifies refraction, stating that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities in the two media, or equivalently, to the indices of refraction.
Mathematically, this is represented as n1sin(i) = n2sin(r). Here ‘i’ is the angle of incidence and ‘r’ is the angle of refraction.
Refraction is the change in direction of a wave passing from one medium to another caused by its change in speed.
This principle applies to other waves too, not just light, such as sound waves or waves in water.

Optical fibres utilise the principle of total internal reflection caused by the differing refractive indices of the core and cladding material to transmit light signals over long distances.
The refractive index of different mediums is crucial in the design of lenses in order to control the bending and focusing of light.
Refractive index is utilised in various scientific and industrial fields, including physics, chemistry, and material science, to identify the properties of substances.