A needle placed 40 cm from a lens forms an image on a screen placed 80 cm on the other side of the lens. Identify the type of lens and determine its focal length. What is the size of the image, if the size of needle is 15 cm ?

Explanation

Lens forms the image of object on the other side of lens
`:.` Given lens is a convex lens
`u=-40cm`
`v=+80cm` `f=?`
We know `1/f=1/v-1/u`
`1/f=1/80-1/(-40)=1/80+1/40`
`1/f=(1+2)/80=3/80`
`f=80/3=6.67cm`
Size of needle `=O=+15cm`
Size of image of needle =I=?
`m=I/O=v/u`
`I=v/u=(O)`
`I=80/(-4)(15)=-30cm`