$A$ convex and a concave lens separated by a distance are then put in contact. How does the focal length of the combination change?

$A$ lens maker has to design an achromatic combination of effective power $-0.5 \, D$. The two types of glasses to be used (say $A$ and $B$) have dispersive powers in the ratio $\omega_A : \omega_B = 3 : 5$. Then the lens made from glass $A$ will have a focal length of ....... $cm$.

$A$ combination of two thin lenses in contact has a power of $+10 D$. The power reduces to $+6 D$ when the lenses are $0.25 m$ apart. The power of each individual lens is:

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 $cm$.

$A$ biconvex lens is formed by using two thin planoconvex lenses, as shown in the figure. The refractive index and radius of curved surfaces are also mentioned in the figure. When an object is placed on the left side of the lens at a distance of $30 \ cm$ from the biconvex lens, the magnification of the image will be:

The focal length (in $cm$) of a lens with dispersive power $0.45$ that should be placed in contact with a convex lens of focal length $84 \,cm$ and dispersive power $0.21$ to form an achromatic combination is: