Two lenses of power $+12 \ D$ and $-2 \ D$ are placed in contact. The combined focal length of the combination will be ....... $cm$.

Two thin convex lenses of focal lengths $30 \ cm$ and $10 \ cm$ are placed coaxially, $1 \ cm$ apart. The power of this combination is (in $D$):

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

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 doublet of two lenses in contact has a power of $+2 \ D$. The convex lens has a power of $+5 \ D$. What is the ratio of the dispersive powers of the convergent and divergent lenses?

Obtain the equation of power and magnification for a combination of lenses.