Question

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.

• A. 12 cm behind convex mirror, real
• B. 9 cm behind convex mirror, real
• C. 6 cm behind convex mirror, virtual
• D. 3 cm behind convex mirror, virtual

Answer 1

Answer: (C)

According to given problem, for concave mirror,
$u=-15 \,cm $ and $f=-10 \,cm$
$\frac{1}{v}+\frac{1}{-15}=\frac{1}{-10}$ i.e., $v=-30 \,cm$
i.e., concave mirror will form real, inverted and enlarged image $I_{1}$ 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 $I_{1}$ will act as an object and so for it $u=-10 \,cm$ and $f=+15 \,cm$.
$\frac{1}{v}+\frac{1}{-10}=\frac{1}{15} $ i.e., $v=+6\, cm$
So final image $I_{2}$ is formed at a distance $6 \,cm$ behind the convex mirror and is virtual as shown in figure.