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.

Explanation

For `M_(1)` mirror `O` act as a object , let its image is `I_(1)` then ,
`u= -15"cm" , f = -10"cm" implies (1)/(v) + (1)/(-15) = (1)/(-10) implies v = -30 "cm"`
Image `I_(1)` will act as a object for mirror `M_(2)` its distance from `M_(2)` .
`u_(1) = -(40 - 30) "cm" = -10"cm"`
so (1)/(v_(1)) + (1)/(u_(1)) = (1)/(f) implies (1)/(v_(1)) - (1)/(10) = (1)/(15) implies v_(1) = +6` "cm"

So final image `I_(2)` is formed at a distance `6` cm behind the convex mirror and is virtual.