The gradient of this graph is the refractive index of the material of the semicircular block. So the ray emerging undergoes no change in direction as it leaves as the emerging ray leaves at 90 ...

We can also use wavelengths to calculate refractive index. By substituting \(v_{1}=f\lambda _{1}\) and \(v_{2}=f\lambda _{2}\) into \(n=\frac{v_{1}}{v_{2}}\) then ...

Vector analysis was used to calculate a correcting refraction, which converts the incorrect refraction to the correct one. These calculations have previously been published by Retzlaff et al.