Lenses are objects made of transparent materials such as glass or clear plastic that have curved surfaces. Diverging lenses are thicker at their edges than at their centres and make light rays passing through them spread out. Converging lenses are thicker in their middle than at their edges and make light rays passing through them focus at a point. These are used in spectacles to help people with poor vision see better. The converging lenses magnify by bending the rays of light that pass through them to meet at a point called focus. The thicker the converging lens is at its centre, the more it magnifies and the closer the focus is to the lens.
$(i)$ Ravi uses two convex lenses $A$ and $B$ of the same size and same material as shown. $P_1$ and $P_2$ are the powers of $A$ and $B$. An object is kept at the same distance from the lens between $F$ and $2F$ of each lens on the principal axis in turn. Let $I_1$ and $I_2$ be the images formed by the two lenses respectively. What is the relation between the image distances of both lenses?
(ii) Write down the relation between the powers of both lenses.
(iii) Meenakshi uses the above two lenses $A$ and $B$ along with another two lenses $C$ and $D$, as shown. She is able to see the subject matter on the blackboard while sitting in the front row in the classroom but is unable to see the same matter while sitting in the last row. Which of the above four lenses will she require to correct the defect in her vision? Why?
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(iv) Natasha places an object on the principal axis of the above given lens $A$. One end of this object coincides with the focus $F$ and the other end with $2F$. What will be the nature of the image formed by the lens on the other side?