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.

According to given problem, for concave mirror,
a = -15 cm and f = -10 cm

$\frac{1}{\mathrm{v}}+\frac{1}{-15}=\frac{1}{-10}\mathrm{i}.\mathrm{e}.,\mathrm{v}=-30\mathrm{cm}$

i.e., concave mirror will form real, inverted and enlarged image 1, of object O at a distance 30 cm from it, 

i.e., at a distance 40 - 30 = 10 cm from convex mirror. 

For convex mirror the image.I, will act as an object and so for it u = -10 cm and f = +15 cm.

$\frac{1}{\mathrm{v}}+\frac{1}{-10}=\frac{1}{15}\mathrm{i}.\mathrm{e}.,\mathrm{v}=+6\mathrm{cm}$

So final image ${\mathrm{I}}_2$, is formed at a distance 6 cm behind the convex mirror and is virtual as shown in figure.