The half-cylinder is made of an optically transparent material with a radially variable refractive index $n$. The dependence of $n$ on the radius $r$ is shown on the graph in coordinates $\ln{n}$ and $\ln{\frac{r}{r_0}}$ where $r_0 = 1$ cm.

Using this dependence, find the radii of the semicircles, along which a thin beam of light can propagate when it normally falls on the flat surface of the half-cylinder.