$A$ convex lens of power $+6 D$ is placed in contact with a concave lens of power $-4 D$. What is the nature and focal length of the combination?

Three lenses $L_1, L_2, L_3$ are placed co-axially as shown in the figure. The focal lengths of the lenses are $30 \, cm, 10 \, cm$ and $5 \, cm$ respectively. If a parallel beam of light falls on lens $L_1$ and emerges from $L_3$ as a convergent beam such that it converges at the focus of $L_3$,find the distance $d$ between $L_1$ and $L_2$ in $cm$.

$A$ concave and a convex lens have the same focal length of $20 \ cm$ and are put into contact to form a lens combination. The combination is used to view an object of $5 \ cm$ length kept at $20 \ cm$ from the lens combination. As compared to the object,the image will be

$A$ convex lens is in contact with a concave lens. The magnitude of the ratio of their focal lengths is $2/3$. Their equivalent focal length is $30 \ cm$. What are their individual focal lengths?

Find the distance of the final image from the object $O$,formed by the combination of lenses shown in the figure (in $cm$):

It is desired to make an achromatic combination of two lenses ($L_1$ and $L_2$) made of materials having dispersive powers $\omega_1$ and $\omega_2$ $(< \omega_1)$. If the combination of lenses is converging,then: