First slide

Plane mirror

Question

A ray of light is incident at 50° on the middle of one of the two mirrors arranged at an angle of 60° between them. The ray then touches the second mirror, get reflected back to the first mirror, making an angle of incidence of

Moderate

A

50°
B

60°
C

70°
D

80°

Solution

Let required angle be $θ$
From geometry of figure
$In △ ABC; α = 180^{\circ} - (60^{\circ} + 40^{\circ}) = 80^{\circ} \Rightarrow β = 90^{\circ} - 80^{\circ} = 10^{\circ} In △ ABD; ∠ A = 60^{\circ}, ∠ B = (α + 2 β) = (80 + 2 \times 10) = 100^{\circ} and ∠ D = (90^{\circ} \bar{θ}) ∵ ∠ A + ∠ B + ∠ D = 180^{\circ} \Rightarrow 60^{\circ} + 100^{\circ} + (90^{\circ} - θ) = 180^{\circ} \Rightarrow θ = 70^{\circ}$

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