Question

two perpendicular plane mirrors are placed as shown in the figure. the light rays AB and CD will be parallel for
options are
any value of theta
theta=45°only
theta>45°only
theta<45°only


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Answer 1

The rays AB AND CD will be parallel for $\theta$ = 45° only.

Proof:

$\angle \: ABX = 45 \degree$

So , as per rules for Reflection , the opposite angle shall also be 45°.

$\therefore \: \angle \: BCZ = 45 \degree$

In ∆BCZ :

$\angle \:ZCB = 180 \degree - 90 \degree - 45 \degree$

$= > \angle \:ZCB = 45 \degree$

So, we can say that :

$= > \angle \: BCP = 90 \degree - \angle \:ZCB$

$= > \angle \: BCP = 90 \degree - 45 \degree$

$= > \angle \: BCP =45 \degree$

As per rules of reflection ,

$= > \angle \: BCP = \angle PCD=45 \degree$

Hence ;

$\therefore \: \angle \: BCD + \angle \: ABC = 90 \degree + 90 \degree$

$= > \: \angle \: BCD + \angle \: ABC = 180 \degree$

So , sum of two internal angles is 180° , hence the lines AB and CD are parallel.