As shown in fig., an object $O$ is at the position $(-10,2)$ with respect to the origin $P$. The concave mirror $M_1$ has radius of curvature $30cm$. A plane mirror $M_2$ is kept at a distance of $40cm$ in front of the concave mirror.

Given: an object O is at the position $(-10,2)$ with respect to the origin P. The concave mirror $M_1$ has radius of curvature 30 cm. A plane mirror $M_2$ is kept at a distance of 40 cm in front of the concave mirror.

To find the coordinates of the second image w.r.t. the origin P considering first reflection on the concave mirror $M_1$ and second on the plane mirror $M_2$

Solution:

For $M_1,u=-10cm,f=-15cm,h=2cm$

Using mirror formula,

$\frac{1}{v}+1u=1f⟹\frac{1}{v}+\frac{1}{-10}=\frac{1}{-15}⟹\frac{1}{v}=\frac{1}{10}-\frac{1}{15}=\frac{3-2}{30}⟹v=30cm$

and $\frac{h_2}{h_1}=\frac{v}{u}⟹h_2=6cm$

Hence, the image formed by the plane mirror is 70 cm below the principal axis and $70+6-30=46cm$ to the left of the mirror.

Therefore, the coordinate s of $I_2$ w.r.t to P is $(-46,-70)$