An object placed $10 \ cm$ in front of a lens has an image $20 \ cm$ behind the lens. What is the power of the lens (in dioptres)?

An object placed at a distance of $16 \ cm$ from a convex lens produces an image of magnification $m$ $(m > 1)$. If the object is moved towards the lens by $8 \ cm$, then again an image of magnification $m$ is obtained. The numerical value of the focal length of the lens is (in $cm$)

$A$ thin glass (refractive index $1.5$) lens has an optical power of $-5 D$ in air. Its optical power in a liquid medium with a refractive index of $1.6$ will be:

An object is placed at a distance $m$ times the focal length of a divergent lens. The size of the image is shorter than that of the object by what factor?

$A$ lens is placed between a source of light and a wall. It forms images of area $A_1$ and $A_2$ on the wall for its two different positions. The area of the source of light is

For a thin convex lens, the radii of curvature are $15 \,cm$ and $30 \,cm$ respectively. The focal length of the lens is $20 \,cm$. The refractive index of the material is: