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Q.

Two plane mirrors are joined together as shown in figure. Two point objects $O_{1}$ and $O_{2}$ are placed symmetrically such that $A O_{1}$ = $A O_{2}$ . The image of the two objects is common if :

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a

$θ = 45^{o}$

b

$θ = 60^{o}$

c

$θ = 30^{o}$

d

$θ = 90^{o}$

answer is B.

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Detailed Solution

Assuming the above condition to be true
As AB is common and $O_{1} B$ = BI
$Δ O_{1} B A a n d Δ B A I a r e c o n g r u e n t$
By symmetry AI is perpendicular to $O_{1} O_{2}$
and $∠ O_{1} A B = ∠ B A I$
$∴ B A I = 45 º$
and $∠ B A C = 90^{0}$

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