Question

A point object O is placed at a distance of 0.3 m from a convex lens of focal length 0.2 m. It is then cut into two halves each of which is displaced by 0.0005 m as shown in figure.

image will be formed from the lens at a distance of

Answer 1

As shown two lenses `L_1` and `L_2` will form two images at `I_1` and `I_2`
Lens formula: `(1)/(v)-(1)/(u)=(1)/(f)`
`(1)/(v)-(1)/(-0.3)=(1)/(0.2)implies(1)/(v)=(1)/(0.2)-(1)/(0.3)=(1)/(0.6)`
`v=0.6m`
In similar triangles `O O_1 O_2` and `O I_1 I_2`
`(O_1O_2)/(|u|)=(I_1I_2)/(|u|+v)`
`(2xx0.0005)/(0.3)=(I_1I_2)/(0.3+0.6)`
`I_1I_2=0.003m`