Question

If incident ray CA and reflected ray BD are parallel to each other. Find the angle of inclination between the mirrors.

• A. $i_1+i_2=\theta$
• B. $i_1+i_2=\frac{1}{2}\theta$
• C. $i_1+i_2=2\theta$
• D. none

Answer 1

The correct option is A $i_1+i_2=\theta$

Since $AC$ and $BD$ are parallle,

hence $\angle BAC+\angle ABD={180}^o$

$⟹2i_1+2i_2={180}^o$

$⟹i_1+i_2={90}^o$

Now, in triangle $\Delta AOB-$

$\alpha ={90}^o-i_1$

$\beta ={90}^o-i_2$

And, $\alpha +\beta +\theta ={180}^o$

$⟹{90}^o-i_1+{90}^o-i_2+\theta ={180}^o$

$⟹\theta =i_1+i_2$

And, $\theta =i_1+i_2={90}^o$

Answer-(A)