Question

Two mirrors are inclined at an angle of ${30}^{\circ }$. An object is placed making an angle of ${10}^{\circ }$ with mirror $M_1$. The position of the second image formed by mirrors $M_1$ and $M_2$ with respect to mirrors $M_1$ and $M_2$ respectively will be

• A. ${50}^{\circ }$ from $M_1$ and ${40}^{\circ }$ from $M_2$
• B. ${30}^{\circ }$ from $M_1$ and ${20}^{\circ }$ from $M_2$
• C. ${70}^{\circ }$ from $M_1$ and ${40}^{\circ }$ from $M_2$
• D. ${10}^{\circ }$ from $M_1$ and ${80}^{\circ }$ from $M_2$

Answer 1

The correct option is A ${50}^{\circ }$ from $M_1$ and ${40}^{\circ }$ from $M_2$

All the images will lie on a circle whose centre is the intersection point of mirrors and radius equal to the distance of the object from the intersection point.
On applying, object angular position $=$ image angular position $w.r.t$ mirror, we get, the images of the object as shown in the figure.

From figure, we can see that second image formed by mirrors $M_1$ and $M_2$ will be at ${50}^{\circ }$ from $M_1$ and at ${40}^{\circ }$ from $M_2$.