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Three plane mirrors are placed such that the angle between the first and second or second and third is the same $' θ'$ . A light striking the first mirror, after reflection at the three mirrors emerges opposite to the initial direction. The value of $' θ' = 30 ° \times x$ , then $x =$

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answer is D.

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Detailed Solution

Angle of incidence I will be same corresponding to the three mirrors. Total deviation

$d = 3 (180 - 2 i);$

$180 = 3 (180 - 2 i)$

$180 - 2 i = 60 \Rightarrow i = 60$

In $Δ APQ, ∠ A = ∠ Q = 90 - i = 30 °$

and $∠ A + θ + ∠ Q=180°$

$\Rightarrow 30+ θ +30=180°$

$\Rightarrow θ = 120°$

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