Question

Light is refracted at the boundary between water and an unknown medium. If the angle of incidence is \(25^{\circ}\), and the angle of refraction is \(20,6^{\circ}\), calculate the refractive index of the unknown medium.

Answer 1

The angle of incidence \(\theta_{1}=25^{\circ}\)
The angle of refraction \(\theta_{2}=20,6^{\circ}\)
\(n_{1}=1,333\)
We need to calculate the refractive index for the unknown medium.

We can use Snell's law to calculate the unknown refractive index, \(n_{2}\)
According to Snell's Law:
\[
\begin{aligned}
n_{1} \sin \theta_{1} &=n_{2} \sin \theta_{2} \\
n_{2} &=\frac{n_{1} \sin \theta_{1}}{\sin \theta_{2}} \\
n_{2} &=\frac{1,333 \sin 25^{\circ}}{\sin 20,6^{\circ}} \\
n_{2} &=1,6
\end{aligned}
\]

Typically glass has a refractive index between 1,5 to 1,9 . Therefore the unknown medium is typical glass.