Refractive Index (Cambridge (CIE) IGCSE Physics): Revision Note

Refractive index as a ratio of speed

Extended Tier Only

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

  • using the ratio of speeds

  • 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:

$n=\frac{\mathrm{speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{a}\mathrm{vacuum}}{\mathrm{speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{a}\mathrm{material}}$

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 refraction of a wave in two different regions

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

$n=\frac{\sin i}{\sin r}$

• 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: