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?

$A$ convex lens has its radii of curvature equal. The focal length of the lens is $f$. If it is divided vertically into two identical plano-convex lenses by cutting it, then the focal length of the plano-convex lens is ($\mu =$ the refractive index of the material of the lens).

The focal length of a biconvex lens made of glass with equal radii of curvature is $f$. If the lens is dipped in water, what will be its new focal length? (Take the refractive index of glass as $3/2$ and water as $4/3$)

If the central portion of a convex lens is wrapped in black paper as shown in the figure,

If the focal length of a double convex lens for red light is $f_R$,what is its focal length for violet light?

$A$ convex lens of focal length $20 \ cm$ produces images of the same magnification $2$ when an object is kept at two distances $x_1$ and $x_2$ $(x_1 > x_2)$ from the lens. The ratio of $x_1$ and $x_2$ is