Question

What should be the angle between the two mirrors so that, whatever may be the angle of incidence, the incident ray and the reflected ray from the two mirrors will be parallel to each other?

• A. ${45}^o$
• B. ${75}^o$
• C. ${90}^o$
• D. ${120}^o$

Answer 1

The correct option is C ${90}^o$

Let the angle between mirrors be $\theta$, then

Deviation $\delta =180-2i_1+180-2i_2$

$=360-2(i_1+i_2)$

For the resultant ray to be parallel, $\delta$ should be ${180}^0$

$\therefore 360-2(i_1+i_2)={180}^0$

$\Rightarrow (i_1+i_2)={90}^0$

From the geometry of figure,
$90-i_1+90-i_2+\theta =180$

$\therefore i_1+i_2=\theta$

Hence, angle between the mirror should be ${90}^0$.