Refractive Index

Refractive Index

The speed of light and therefore the degree of bending of the light depends on the refractive index of material through which the light passes. The refractive index (symbol $$n$$) is the ratio of the speed of light in a vacuum to its speed in the material.

Definition: Refractive index

The refractive index (symbol $$n$$) of a material is the ratio of the speed of light in a vacuum to its speed in the material and gives an indication of how difficult it is for light to get through the material.

$n = \frac{c}{v}$ where $\begin{array}{rl} n &= \text{refractive index (no unit)} \\ c &= \text{speed of light in a vacuum } (\text{3.00} \times \text{10}^{\text{8}}\text{ m·s^{-1}}) \\ v &= \text{speed of light in a given medium } (\text{m·s^{-1}}) \\ \end{array}$

Using the definition of refractive index $n = \frac{c}{v}$ we can see how the speed of light changes in different media, because the speed of light in a vacuum, $$c$$, is constant.

If the refractive index, $$n$$, increases, the speed of light in the material, $$v$$, must decrease. Therefore light travels slower through materials of high refractive index, $$n$$.

The table below shows refractive indices for various materials. Light travels slower in any material than it does in a vacuum, so all values for $$n$$ are greater than $$\text{1}$$.

 Medium Refractive Index Vacuum $$\text{1}$$ Helium $$\text{1.000036}$$ Air* $$\text{1.0002926}$$ Carbon dioxide $$\text{1.00045}$$ Water: Ice $$\text{1.31}$$ Water: Liquid ($$\text{20}$$$$\text{°C}$$) $$\text{1.333}$$ Acetone $$\text{1.36}$$ Ethyl Alcohol (Ethanol) $$\text{1.36}$$ Sugar solution ($$\text{30}\%$$) $$\text{1.38}$$ Fused quartz $$\text{1.46}$$ Glycerine $$\text{1.4729}$$ Sugar solution ($$\text{80}\%$$) $$\text{1.49}$$ Rock salt $$\text{1.516}$$ Crown Glass $$\text{1.52}$$ Sodium chloride $$\text{1.54}$$ Polystyrene $$\text{1.55}$$ to $$\text{1.59}$$ Bromine $$\text{1.661}$$ Sapphire $$\text{1.77}$$ Glass (typical) $$\text{1.5}$$ to $$\text{1.9}$$ Cubic zirconia $$\text{2.15}$$ to $$\text{2.18}$$ Diamond $$\text{2.419}$$ Silicon $$\text{4.01}$$
Table: Refractive indices of some materials. $$n_{\text{air}}$$ is calculated at standard temperature and pressure (STP).

Example: Refractive Index

Question

Calculate the speed of light through glycerine which has a refractive index of $$\text{1.4729}$$.

Step 1: Determine what is given and what is required

We are given the refractive index, $$n$$ of glycerine and we need to calculate the speed of light in glycerine.

Step 2: Determine how to approach the problem

We can use the definition of refractive index since the speed of light in vacuum is a constant and we know the value of glycerine’s refractive index.

Step 3: Do the calculation

$n = \frac{c}{v}$Rearrange the equation to solve for $$v$$ and substitute in the known values: \begin{align*} v &= \frac{c}{n} \\ &= \frac{\text{3} \times \text{10}^{\text{8}}\text{ m·s$^{-1}$}}{\text{1.4729}} \\ &= \text{2.04} \times \text{10}^{\text{8}}\text{ m·s$^{-1}$} \end{align*}