Refractive index of negative 1

An infinitely long cylinder of radius $R$ is made of an unusual exotic material with refractive index –1. The cylinder is placed between two planes whose normal's are along the $y$ direction. The center of the cylinder $O$ lies along the $y$ -axis. A narrow laser beam is directed along the $y$ direction from the lower plate. The laser source is at a horizontal distance $x$ from the diameter in the $y$ direction. Find the range of $x$ such that light emitted from the lower plane does not reach the upper plane.

$\rightarrow \large \frac{n_1 R \pi}{8} \leq R \leq \frac{n_2 R \pi}{8}$ .

Find the value of $n_1 + n_2$ .