A concave mirror of focal length 10 cm and a convex mirror of focal length 15 cm are placed facing each other 40 cm apart. A point object is placed between the mirrors, on their common axis and 15 cm from the concave mirror. Find the position and nature of the image produced by the successive reflections, first at concave mirror and then at convex mirror. 

Concave mirror : From P₁, rightwards is –ve leftwards is +ve  
u = –15cm, V = ?, f = – 10 cm 

$$\begin{gathered} \frac{1}{\mathrm{V}}+\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}}\Rightarrow \frac{1}{\mathrm{V}}-\frac{1}{15}=-\frac{1}{10} \\ \Rightarrow \mathrm{V}=-30\mathrm{cm} \end{gathered}$$
I₁ is the real image formed by concave mirror. It acts as real object to the convex mirror.

$\text{For Convex mirror : }\mathrm{u}=-10\mathrm{cm},\mathrm{f}=+15\mathrm{cm},\mathrm{V}=\text{ ? }$ 
$\left[\text{ From }{\mathrm{P}}_2\right.\text{, leftwards is -ve, rightwards in +ve] }$
$\frac{1}{\mathrm{V}}+\frac{1}{-10}=\frac{1}{15}\Rightarrow \mathrm{V}=+6\mathrm{cm}$
I₂ is the virtual image formed by convex mirror.