Question

A concave mirror of focal length 10cm and a convex mirror of focal length 15cm are placed facing each other 40cm apart. A point object is placed between the mirrors, on their common axis and 15cm from the concave mirror. Find the position and nature of the image produced by successive reflections, first at the concave mirror and then at the convex mirror.
A. 12cm behind convex mirror, real
B. 9cm behind convex mirror, real
C. 6cm behind convex mirror, virtual
D. 3cm behind convex mirror, virtual

Answer 1

Correct Answer - c.
According to given problem, for concave mirror,
`u=-15cm` and `f=-10cm`
`(1)/(v)+(1)/(-15)=(1)/(-10), i.e, v=-30cm`
i.e., concave mirror will form real, inverted, and enlarged image `I_(1)` of object O at a distance of 30cm from it, i.e., at a distance `40-30=10cm` from the convex mirror.
For convex mirror, the image `I_(1)` will act as an object and so for it `u=-10cm ` and `f=+15cm`.
`(1)/(v)+(1)/(-10)=(1)/(15), i.e., v=+6cm`
So, final image `I_(2)` is formed at a distance of 6cm behind the convex mirror and is virtual as shown in figure .