Question

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.

Answer 1

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

Now |θ_i|=|θ_r|=|θ'_r|

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

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