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.

Options

A. `12 cm` behind convex mirrorr, real
B. `9 cm` behind convex mirrorr, real
C. `6 cm` behind convex mirrorr, virtual
D. `3 cm` behind convex mirrorr, virtual

Answer

C

Explanation

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