Two concave mirrors are places 40cm apart and are facing each other. A point object lies between them at a distance of 12cm from the mirror of focal length 10cm. The other mirror has a focal length of 15cm. Find the location of final image formed after two reflections - first at the mirror nearer to the object and second at the other mirror.

Explanation

First reflection: As incident rays are directed toward left, all quantities to the left of plane are taken positive.
`u_(1)=-12cm, f_(1)=-10cm`
`v_(1)=(u_(1)f_(1))/(u_(1)-f_(1))=(120)/(-12+10)=-60cm`
The rays after reflection are going to converge at a point `I_1 = 60` from the first mirror, i.e., `60-40 = 20 cm` behind the other mirror.
Second reflection: As incident rays are directed toward right, all quantities towards right will be taken positive.
The converging rays falling at the second mirror create a virtual object for this mirror at `I_(1)` with the object distance
`u_(2)=+20cm` and `f_(2) =-15cm,`
`v_(2)=(u_(2)f_(2))/(u_(2)-f_(2))=(-20xx15)/(+20+15)=(-300)/(35)=-8.57cm`
As right is positive, image will be formed to the left of mirror.
Hence, the final image is formed at a distance of `8.57 cm` from the second mirror and is real.