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

According to given problem, for concave mirror, u=-15 cm and f=-10 cm
So `(1)/(v ) +(1)/(-15 )=(1)/(-10) , i.e., V=-30cm`
i.e., concave mirror will form real, inverted and enlarged image I, 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=+15cm.
`(1)/(v) +(1)/(-10) =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
Over all magnification `= m_1 xx m_2 =-2 xx 6//10 = -6//5` Negative indicates final image is inverted w.r.t given object.