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  4. Two plane mirrors are inclined at an angle θ . It is found that a ray incident on one mirror at any angle is rendered parallel to itself after reflection from both the mirrors. The value of θ is

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Q. Two plane mirrors are inclined at an angle $ \theta $ . It is found that a ray incident on one mirror at any angle is rendered parallel to itself after reflection from both the mirrors. The value of $ \theta $ is

UPSEEUPSEE 2009

Solution:

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Incident ray and finally reflected ray are parallel to each other means $\delta=180^{\circ}$
From $\delta=360^{\circ}-2 \theta$
$\Rightarrow 180^{\circ}=360^{\circ}-2 \theta$
$\Rightarrow \theta=90^{\circ}$