Waves: Refractive Index

The refractive index is a measure of how much a wave is refracted (bent) when it enters a medium.
It is a dimensionless number and is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium.
The equation for refractive index (n) is n = c/v, where c is the speed of light in a vacuum and v is the speed of light in the medium.
When light enters a medium with a higher refractive index (e.g., from air to glass), it slows down and the ray bends towards the normal line.
Conversely, when light leaves a medium with a higher refractive index (e.g., from glass to air), it speeds up and the ray bends away from the normal line.
The angle of incidence and the angle of refraction are related by Snell’s law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the refractive index.
If the angle of incidence is greater than the critical angle, total internal reflexion will occur. This is used in fibre optics and the operation of binoculars, periscopes, and other optical devices.
For a given set of two materials, the refractive index will be different based on the frequency of light. This principle is used in dispersion of light, e.g. in a prism, where different colours (frequencies) of light are refracted by different amounts.
The refractive index of a vacuum and air are nearly the same, and are typically approximated as 1 in calculations.
The refractive index of water is about 1.33 and the refractive index of glass ranges from about 1.4 to 1.6.
Always draw a normal line at 90 degrees to the boundary at the point where light hits. This helps in accurate measurement of angles. Remember, angles of incidence and refraction are measured from the normal, not the boundary surface.