A monochromatic beam of light enters a square | vedclass

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(C) For the light beam to exit through the same hole after reflecting off every other wall exactly once,the path must be symmetric with respect to the

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The beam will come out only at $	heta_i=45^{\circ}$.

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(C) For the light beam to exit through the same hole after reflecting off every other wall exactly once,the path must be symmetric with respect to the diagonal of the square. Let the angle of incidence be $	heta_i$. The angle of reflection at the first wall will also be $	heta_i$. By tracing the path through the square,the geometry requires that the angle of incidence at the subsequent walls leads to a path that returns to the opening at an angle of exit $e = 	heta_i$. For the beam to exit through the same hole after hitting all three other walls,the total deviation must be such that the beam is parallel to its original path but reversed,or follows a symmetric path. In a square enclosure,for the light to hit all three walls and return to the opening,the geometry dictates that the angle $	heta_i$ must satisfy the condition $2	heta_i = 90^{\circ}$,which gives $	heta_i = 45^{\circ}$. Thus,the beam will come out only at $	heta_i = 45^{\circ}$.

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