Refractive Index (Cambridge (CIE) IGCSE Physics)

Refractive index as a ratio of speed

Extended tier only

• The refractive index can be calculated in two different ways:

1. Using the ratio of speeds

2. Using the ratio of angles

• The refractive index is a number that is always larger than 1 and is different for different materials

  • Objects which are more optically dense have a higher refractive index, e.g. n is about 2.4 for diamond

  • Objects which are less optically dense have a lower refractive index, e.g. n is about 1.5 for glass

• Since the refractive index is a ratio, it has no units

• The refractive index, n, for the ratio of speeds, is defined as:

The ratio of the speeds of a wave in two different regions

• The refractive index, n, for the ratio of speeds, is given by the equation:

Refractive index as a ratio of angles

Extended tier only

• The refractive index, n, for the ratio of angles, is defined as:

The ratio of the sine of the angle of incidence and the sine of the angle of reflection of a wave in two different regions

• The refractive index, n, for the ratio of angles, is given by the equation:

• Where:

  • n = the refractive index of the material

  • i = angle of incidence of the light (°)

  • r = angle of refraction of the light (°)

• This equation can be rearranged with the help of the formula triangle:

A refractive index formula triangle

Formula triangle for the refractive index in terms of angles

• See the example of Speed & velocity which explains how to use the formula triangle to rearrange equations