Determine the Index of Refraction from Refraction Data

The index of refraction for air is taken to be 1 in most cases (and up to four significant figures, it is 1.000). Thus $n_1=1\text{.}\text{00}$ here. From the given information, ${\theta }_1=\text{30}\text{.}\mathrm{0º}$ and ${\theta }_2=\text{22}\text{.}\mathrm{0º}$. With this information, the only unknown in Snell’s law is $n_2$, so that it can be used to find this unknown.

Snell’s law is

Rearranging to isolate $n_2$ gives

Entering known values,

This is the index of refraction for water, and Snell could have determined it by measuring the angles and performing this calculation. He would then have found 1.33 to be the appropriate index of refraction for water in all other situations, such as when a ray passes from water to glass. Today we can verify that the index of refraction is related to the speed of light in a medium by measuring that speed directly.