Question

An infinitely long cylinder of radius is made of an unusual exotic material with refractive index -1 (Figure). The cylinder is placed between two planes whose normals are along the y direction. The centre of the cylinder 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 from the diameter in the y direction. Find the range of such that light emitted from the lower plane does not reach the upper plane

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Updated on : 2022-09-05
Solution
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As the cylinder is made of refractive index and is placed in air of , so when ray is incident at B to cyliner, will be negative ie., refractive ray will get reflected from normal. Similar thing happens at incidence point and angle of refraction and incident at and will be equal as and of refraction at is
as reflection takes place
The total deviation of out-coming ray from the incoming ray . Rays shall not reach the receiving plane if angles measured clockwise from the y axis
or (on dividing by 4 to all sides)
Thus for light emitted from the source shall not reach the receiving plane if

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