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  • Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror and parallel to the second is reflected from the second mirror parallel to the first mirror. Deter

Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror and parallel to the second is reflected from the second mirror parallel to the first mirror. Determine the angle between the two mirrors.

Option: 1

60^{\circ}


Option: 2

30^{\circ}


Option: 3

90^{\circ}


Option: 4

180^{\circ}


Answers (1)

best_answer

Let \theta be the angle between the two mirrors \mathrm{O_{1}} and \mathrm{O_{2}}. The incident ray \mathrm{AB} is parallel to mirror \mathrm{OM}_{2} and strikes the mirror \mathrm{OM}_{1} at an angle of incidence equal to \alpha. From figure we have

\angle \mathrm{M}_{1} \mathrm{BA}=\angle \mathrm{OBC}=\angle \mathrm{M}_{1} \mathrm{OM}_{2}=\theta


Similarly for reflection at mirror \mathrm{OM}_{2}, we have
\angle \mathrm{M}_{2} \mathrm{CD}=\angle \mathrm{BCO}=\angle \mathrm{M}_{2} \mathrm{OM}_{1}=\theta

Now in triangle \mathrm{OBC}, 3 \theta=180^{\circ} , therefore
\theta=60^{\circ}

Posted by

avinash.dongre

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