What is a lens?

The size of the images of an object,formed by a thin lens,are equal when the object is placed at two different positions $8 \ cm$ and $24 \ cm$ from the lens. The focal length of the lens is . . . . . . $cm$.

$A$ thin converging lens of focal length $f=25 \,cm$ forms the image of an object on a screen placed at a distance of $75 \,cm$ from the lens. The screen is moved closer to the lens by a distance of $25 \,cm$. The distance through which the object has to be shifted,so that its image on the screen is sharp again,is (in $\,cm$)

$A$ substance is behaving as a convex lens in air and a concave lens in water. What is its refractive index?

An object of size $3.0 \, cm$ is placed $14 \, cm$ in front of a concave lens of focal length $21 \, cm$. Describe the image produced by the lens. What happens if the object is moved further away from the lens?

When a biconvex lens of glass having refractive index $1.47$ is dipped in a liquid,it acts as a plane sheet of glass. This implies that the liquid must have a refractive index: