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 normals are along the y-direction. The centre 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.

The refractive index of the cylinder is -1 and is placed in the air of μ = 1

AB is incident at B to the cylinder such that θr will be negative

θ1= θi = θr

Total deviation of the outcoming ray is 4θ1.

When the angles are measured clockwise, the planes π/3 ≤ 4θ ≤ 3 π/2

If the plane is at R π/r ≤ x ≤ 3R π/8, the light emitted from the source shall not reach the plane.