A point object O is placed at a distance of 30 cm from a convex lens of focal length 20 cm cut into two halves each of which is displaced by 0.05 cm as shown in figure. Find the position of the image. If more than one image is formed, find their number and distance between them.

Explanation

Considering each part as separate lens with u = -30 cm and f = 20 cm, from lens-formula.
`(1)/(v )-(1)/(u ) =(1)/(f) `
we have `(1)/(v ) -(1)/(-30) = (1)/(20) `
i.e., v = 60 cm

So each part will form a real image of the point object O at 60 cm from the lens as shown in figure. As there are two pieces, two images are formed. Now in similar triangles `OI_1 I_2 and OL_1 L_2`
`(I_1 I_2)/(L_1 L_2) = (OP)/(OQ) = ((u +v))/(u )`
i.e.,` I_1 I_2 =(90)/(30) xx(2 xx 0.05 )= 0.3cm `
So the two images formed are 0.3 cm apart.