A plane mirror and a concave mirror are arranged as shown in figure and O is a point object. If the position of image formed by two reflections, (first one taking place at concave mirror) is  $x$cm below point A. Find $x$

 

For concave mirror, $\frac{1}{\upsilon }+\frac{1}{u}=\frac{1}{f}$

$$\begin{gathered} or\frac{1}{\upsilon }-\frac{1}{110}=-\frac{1}{100} \\ or \upsilon =-1100cm \end{gathered}$$

b)  

Thus, first image $I_1$ is formed at 100 cm behind the pale mirror. This acts as virtual object for 
The plane mirror. If plane mirror would had been in vertical position as shown in figure (a),
The image of $I_1$, had been formed at $I_2$,100 cm in front of plane mirror. But since the plane
Mirror has been rotated $45°$ in clockwise direction. Hence, all the reflected rays will Rotate $90°$ in the same sense i.e., clockwise and the image will be formed 100 cm vertically below A.