A converging lens and a converging mirror are placed with their principal axis coinciding. Their separation equals 40cm. A point source S is placed on the principal axis at a distance of 12 cm from the lens as shown in Fig. It is found that the final beam comes out parallel to the principal axis. Focal length of the lens equals 15 cm. Find the focal length of the mirror.

Explanation

Refraction from lens ` (1)/(f_(L))=(1)/(v)-(1)/(u)`
`(1)/(15)=(1)/(v)+(1)/(12)[f_(L)=15, u=-12cm]`
`(1)/(15)-(1)/(12)=(1)/(v)rArrv_(1)=-60cm`
Reflection form mirror: `u_(1)` for mirror `u_(2)=-100 cm`
If finally rays come parallel to principal axis, then the object should be at focus between mirror and lens. Then image created by mirror will `v=-25 cm ` from the pole of mirror for mirror.
For mirror, `(1)/(f_(m))=(1)/(u)+(1)/(v)`
`(1)/(f_(m))=-(1)/(100)-(1)/(25)=-((1+u)/(100))`
`F_(m)=-20cm`