Where should an object be placed in front of a convex lens to obtain an image on the same side as the object?

$A$ point object is placed at a distance of $12 \, cm$ from a convex lens on its principal axis. Its image is formed on the other side of the lens at a distance of $18 \, cm$ from the lens. Find the focal length of the lens. Is the image magnified? Justify your answer.

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.

The figure below shows an object $AB$ placed on the principal axis of a lens $L$. The two foci of the lens are $F_1$ and $F_2$. The image formed by the lens is erect,virtual and diminished. Copy the diagram and answer the following questions: $(i)$ Draw the outline of the lens $(L)$ used. $(ii)$ Draw a ray from $B$ passing through $O$. Show the ray after refraction by the lens. $(iii)$ Draw a ray of light starting from $B$,which after passing parallel to the principal axis,is incident on the lens and emerges after refraction from it. $(iv)$ Locate the final image formed.

$(a)$ Define power of a lens and write its $SI$ unit.
$(b)$ $A$ convex lens forms a real and inverted image of a needle at a distance of $50\, cm$ from it. Where is the needle placed in front of the lens, if the image size is equal to the object size? Also, find the power of the lens.

What is a lens?