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Question
Two mirrors are inclined at an angle θ as shown in the figure. A light ray is incident parallel to one of the mirrors. What should be the value of θ such that the light will retrace its path after the third reflection?
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Solution
It is clear that for third reflection the ray must hit the mirror normally, i.e., the angle of reflection =0∘.
In Δ OBC, ∠OBC=90∘−θ
∴∠CBN=θ
Now, in Δ ABC, θ+θ+θ+90∘=180∘
⇒θ=30∘.
In Δ OBC, ∠OBC=90∘−θ
∴∠CBN=θ
Now, in Δ ABC, θ+θ+θ+90∘=180∘
⇒θ=30∘.
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