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 \(n_1 + n_2\).

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