One half of a convex lens is covered with a black paper.
$(a)$ Show the formation of the image of an object placed at $2F_{1}$ of such a covered lens with the help of a ray diagram. Mention the position and nature of the image.
$(b)$ Draw the ray diagram for the same object at the same position in front of the same lens,but now uncovered. Will there be any difference in the image obtained in the two cases? Give a reason for your answer.

(N/A) The image formed is as shown in the ray diagram. Every part of a lens contributes to the formation of an image. Therefore,if the lower half of the lens is covered,it will still form a complete,real,and inverted image at $2F_{2}$ of the same size as the object on the other side of the lens. However,the intensity (brightness) of the image will be reduced because less light passes through the lens.
$(b)$ In the second case (uncovered lens),the image will be real,inverted,formed at $2F_{2}$,and will have the same size as the object. Its intensity will be greater than the image formed in the first case because more light rays are refracted through the entire aperture of the lens. The diagram is as shown.