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

Image by concave mirror: the direction of incident rays is from left to right.
`u=-15cm,f=-10cm,v=?`
`(1)/(v)+(1)/(u)=(1)/(f)implies(1)/(v)+(1)/(-15)=(1)/(-10)`
`(1)/(v)=-(1)/(10)+(1)/(15)=(-3+2)/(30)=-(1)/(30)`
`v=-30cm`
Image of O is formed at `I_1`
Image by convex mirror: after every reflection, direction of incident rays is recersed, now it is from right to left. Now `I_1` servers as an object for convex mirror.
`u^(')=-10cm,f^(')=15cm,v^(')=?`
`(1)/(v^('))+(1)/(u^('))=(1)/(f^('))implies(1)/(v^(1))+(1)/(-10)=(1)/(15)`
`(1)/(v^('))=(1)/(15)+(1)/(10)+(1)/(10)=(2+3)/(30)=(1)/(6)`
`v^(')=6cm`