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An infinitely long cylinder of radius R is made of an unusual exotic material with refractive index –1 (Fig. 9.7). The cylinder is placed between two planes whose normals 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.

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As the material is of refractive index –1, θr is negative and θ'r positive.

Now |θi|=|θr|=|θ'r|

The total deviation of the outcoming ray from the incoming ray is 4θr. Rays shall not reach the receiving plate if

light emitted from the source shall not reach the receiving plate.

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