A convex lens forms a real image of pencil at a distance of 50 cm from the lens . The image formed is of the same size as the object . Find the focal length and power of the lens. At what distance is the pencil placed from the lens ?

Explanation

Data : Convex lens ,v=50 cm
`M=-1 ,f= ? "h"_(1)=? , u=?`
`M=-1=v/u`
`therefore u=-v=-50cm" " `(object distance)
The pencil is placed at 50 cm from the convex lens . `1/f=1/v-1/u=1/(50cm)-1/(-50cm) =(2)/(50 cm)`
`therefore f=(50cm)/(2)=25 cm`
`P=1/f=1/(25cm)=1/(0.25 m)=4 D`
The power of the lens =4 D.