Refractive Index

Topic Content:

Refractive Index Based on Speed of Light:

Fig. 5.2.1 above shows the ray diagram of light travelling from air to glass. Light travels in air at the rate of 3 × 10⁸ m/s, but as the ray of light hits the glass its speed slows down to 2 × 10⁸ m/s. Due to the change in speed, the light bends towards the normal, i.e. it changes its direction from its original path.

The velocity varies as it travels from one medium to another

In terms of velocity, the refractive index can be defined as:

  \(\scriptsize n = \normalsize \frac{Velocity \; of \; light \; in \; vacuum\:(air)}{Velocity \; of \; light \; in \; glass} \\ = \normalsize \frac{c}{v} \)

where:

• c represents the speed of light in vacuumA vacuum is an area of space containing little or no matter (solids, liquids, and gases). It is a space with nothing in it, not even air. More or air
• v represents the speed of light in the material (glass)

This formula can be used to calculate the refractive index of the material light is travelling to, from air.

For example, we can determine the refractive index of glass (Fig. 5.2.1). For a light travelling from air to glass, the refractive index is:

\( _an_g = \normalsize \frac{Velocity \; of \; light \; in \; vacuum\:(air)}{Velocity \; of \; light \; in \; glass} \\ = \normalsize \frac{c}{v} \\ = \frac {3 \: \times \: 10^8 \: m/s}{2 \: \times \: 10^8 \: m/s} \\ = \frac{3}{2} \\ = \scriptsize 1.5\)

• \( _an_g \)– refractive index of glass with respect to air

Refractive index is a ratio and has no units.