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Standard VII

Physics

Reflection

Two plane mir...

Question

Two plane mirrors $M_{1}$ and $M_{2}$ are inclined at angle $θ$ as shown in the figure. A ray of light l, which is parallel to $M_{1}$ strikes $M_{2}$ and after two reflections, the ray 2 becomes parallel to $M_{2}$ . The angle $θ$ is

0

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30

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45

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60

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Solution

The correct option is C $60$
$α = 90 ° - θ β = θ$
$⟹ θ + β + γ = 180 °$ $($ In $△)$
$⟹ θ + θ + γ = 180 ° ∴ γ = 180 ° - 2 θ$
$∵ δ = 90 ° - γ ∴ δ = 90 ° - (180 ° - 2 θ) = 2 θ - 90 ° θ = 90 ° - δ = 90 ° - (2 θ - 90 °) ⟹ θ = 180 ° - 2 θ ⟹ 3 θ = 180 ° ∴ θ = 60 °$

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