Two lenses of power $+10 \, D$ and $-5 \, D$ are placed in contact. Where should an object be held from the lens so as to obtain a virtual image of magnification $2$ (in $, cm$)?

$A$ 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 .........$cm$.

$A$ convex lens of focal length $30\, cm$ and a concave lens of focal length $10\, cm$ are placed coaxially at a distance $d$ apart. Parallel rays are incident on the convex lens. The rays emerging from the concave lens are also parallel. Then $d = $ . . . . . . $cm$.

$A$ lens of power $3.5 \, D$ is placed in contact with a lens of power $-2.5 \, D$. The combination behaves as:

The ray diagram for two lenses kept at some distance is given in the figure. Which of the following options is correct? ($f_1, f_2 =$ focal lengths,$d =$ distance between lenses)

An achromatic convergent lens of focal length $20 \, cm$ is made of two lenses (in contact) of materials having dispersive powers in the ratio of $1 : 2$ and having focal lengths $f_1$ and $f_2$. Which of the following is true?