First slide

Ray optics

Question

Two plane mirrors are inclined to each other at an angle $θ$ . A ray of light is incident an one mirror and after two successive reflections, the final reflected ray becomes parallel to the incident ray. Then the value of $θ$ is

Moderate

A

Any angle
B

90^o
C

45^o
D

60^o

Solution

$\begin{array}{l} ∠ ABO = π - (α + θ) \\ ∠ RBO = π - (α + θ) \end{array}$
Also, by law of reflection, $∠ {PBM}_{2} = ∠ ABO = π - (α + θ)$
Since PB and QA are parallel, $∠ QAB = ∠ PBR$
$\Rightarrow (π - 2 α) = 2 [π - (α + θ)] \Rightarrow θ = 90^{o}$

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