A biconvex thin lens is prepared from glass `(mu=1.5)`, the two bounding surfaces having equal radii of 25 cm each. One of the surfaces is silvered from outside to make it reflecting. Whee should an object be placed before this lens so that the image is formed on the object itself?

Explanation

we have,`1/f=(mu-1)[1/R_(1)-1/R_(2)]`
`1/f=(3/2-1)(1/30-1/30)=(1/2)(2/30)rArrf=30 cm`
The image of lens should be formed at centre of curvature of mirror.
`1/v-1/u=1/frArr1/(-30)-1/(-x)=1/(30)rArrx=15.5 cm`
Alternatively

`1/F=1/(f_(1))+1/(f_(m))+1/(f_(1))=2/(f_(1))+1/(f_(m))`
`=2/30+1/(30//2)=4/30`
`F=30/4cm`
Since, object and image coincides, u=x=2F=15 cm