Snell's law from geometrical optics states that the ratio of the angles of incidence $\theta_1$ and of the angle of refraction $\theta_2$ as shown in figure1, is the same as the opposite ratio of the indices of refraction $n_1$ and $n_2$.
$$ \frac{\sin\theta_1}{\sin \theta_2} = \frac{n_2}{n_1} $$
(figure originally from wikimedia)
Now let $P$ be a point in one medium (with refraction index $n_1$) and $Q$ a point in the other one as in the figure. My question is, is there is a nice geometrical construction (at best using only ruler and compass) to find the point $O$ in the figure such that Snell's law is satisfied. (Suppose you know the interface and $n_2/n_1$)?
Edit A long time ago user17762 announced to post a construction. However until now no simple construction was given by anybody. So, does anybody know how to do this?