# 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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