Use the values given in Table 5.1, and the definition of refractive index to calculate the speed of light in water (ice).
We look in Table 5.1 and find that the refractive index of water (ice) is \(\text{1,31}\). So the speed of light in ice is:
\begin{align*}
v &= \frac{c}{n} \\
&= \frac{\text{3} \times \text{10}^{\text{8}}\text{ m·s$^{-1}$}}{\text{1,31}} \\
&= \text{2,29} \times \text{10}^{\text{8}}\text{ m·s$^{-1}$}
\end{align*}
Calculate the refractive index of an unknown substance where the speed of light through the substance is \(\text{1,974} \times \text{10}^{\text{8}}\) \(\text{m·s$^{-1}$}\). Round off your answer to 2 decimal places. Using Table 5.1, identify what the unknown substance is.
We are told that the speed of light in the unknown substance is: \(\text{1,974} \times \text{10}^{\text{8}}\) \(\text{m·s$^{-1}$}\). We use this to find the refractive index of the substance:
\begin{align*}
v &= \frac{c}{n} \\
n &= \frac{c}{v} \\
&= \frac{\text{3} \times \text{10}^{\text{8}}\text{ m·s$^{-1}$}}{\text{1,974} \times \text{10}^{\text{8}}\text{ m·s$^{-1}$}} \\
&= \text{1,52}
\end{align*}
We look on Table 5.1 for the substance that has this refractive index and find that the substance is crown glass.