question_answer 66)

  An Infinitely long cylinder of radius R is made of an unusual exotic material with refractive index (-1), Fig. 6(EP). 17. The cylinder is placed between two planes whose normals are along the y directions. 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 light emitted from the lower plane does not reach the upper plane.

Answer:

                    The set up described in the question is shown in Fig. 6(EP). 17. The full line circle represents cross section of infinitely long cylinder of radius R. As the material is of refractive index (- 1), therefore, ,. is positive Also,             For the incoming ray along Y-axis from the lower plane, total deviation of the out coming ray is . The rays shall not reach the receiving plate if (angles are measured clockwise from Y-axis) Or           From Fig. 6(EP).17, sin , when small.             or Hence, we conclude that for values of x lying between and , light emitted  from the laser source shall not reach the upper receiving plane.