Refractive Index

A material’s refractive index (n) is the ratio of the speed of light (c) within a vacuum to the material’s velocity of light (cs):

n = c / cs

The refractive index of a material is never lower than 1. For example:

glass has a refractive index of 1.5
water has a refractive index of 1.33
air as a refractive index of 1

If a ray of light travels through one material into another as opposed to from a vacuum into a material then this is known as relative refractive index.

Relative refractive index

As opposed to the refractive index, the relative refractive index can be lower than 1. When light travels from material 1 with refractive index n1 and into material 2 with refractive index n2 there are a number of way in which the relative refractive index (1n2) can be worked out:

divide the speed of light in material 1 (c1) by the speed of light in material 1 (c2)
divide the refractive index of material 2 (n2) by the refractive index of material 1 (n1)
dive the sine of the incident angle (?1) by the sine of the refracted angle (?2)

1n2 = c1 / c2 = n2 / n1 = sin?1 / sin?2

It is possible rearrange the last part of the equation:

n1sin?1 = n2sin?2

When the direction of light from material 2 intro material 1 is reversed, the new refractive index, 2n1, is related to 1n2 as follows:

2n1 = 1 / 1n2

If a ray of light travels from a material and into an optically less dense material, for example air, then it is possible for the angle of refraction to become 90