$A$ point object,$O$ is placed in front of two thin symmetrical coaxial convex lenses $L_1$ and $L_2$ with focal lengths $24\,cm$ and $9\,cm$ respectively. The distance between the two lenses is $10\,cm$ and the object is placed $6\,cm$ away from lens $L_1$ as shown in the figure. The distance between the object and the image formed by the system of two lenses is .........$cm$.

Two lenses have focal lengths of $+10 \ cm$ and $-15 \ cm$. When they are placed in contact,the combination acts as a convex lens. If the chromatic aberration is zero,what is the ratio of their dispersive powers?

As shown in the figure, a combination of a thin plano-concave lens and a thin plano-convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is $30\,cm$ and the refractive index of the material for both the lenses is $1.75$. Both the lenses are placed at a distance of $40\,cm$ from each other. Due to the combination, the image of the object is formed at a distance $x = ..........cm$ from the concave lens.

$A$ convex lens of focal length $40 \ cm$ is in contact with a concave lens of focal length $25 \ cm$. The power of the combination is:

The given lens is broken into four parts and rearranged as shown. If the initial focal length is $f$,then after rearrangement,the equivalent focal length is

Find the position of the image formed by the lens combination given in the figure.