An object of height 5 cm is held 20 cm away from a convergin lens of focal length 10 cm . Find the position , nature and size of the image formed.

Explanation

Data : Converging lens (convex lens), `f=10cm , h_(1)=5 cm , u=-20 cm, v= ? , h_(2)= ? `
(i) `1/f =1/v -1/u`
`therefore 1/v+1/f=1/u=1/(10cm)+(1)/((-20 cm)`
`=(1)/(10cm)-(1)/(20cm)=(2-1)/(20cm)`
`=(1)/(20 cm)`
`therefore v=20 cm`
The image is real and inverted . It is formed at 20 cm from the lens and on the other side of the lens relative to the object.
(ii) `(h_(2))/(h_(1))=v/u therefore h_(2)=h_(1) ((v)/(u))`
`therefore h_(2)=5 cm xx (20 cm)/(-20cm)=-5 cm`
The height of the image , `h_(2)=-5cm` Thus, it is numberically the same as the heigth of the object.