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?

In a certain camera,a combination of four similar thin convex lenses are arranged axially in contact. Then the power of the combination and the total magnification in comparison to the power $(p)$ and magnification $(m)$ for each lens will be,respectively

$A$ convex lens and a concave lens,each having the same focal length of $25\, cm$,are put in contact to form a combination of lenses. The power in diopters of the combination is:

$A$ bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. The refractive index $n$ of the first lens is $1.5$ and that of the second lens is $1.2$. Both the curved surfaces have the same radius of curvature $R = 14 \ cm$. For this bi-convex lens,if the object distance is $40 \ cm$,what will be the image distance (in $cm$)?

An object is placed $0.40 \,m$ from one of the two lenses $L_1$ and $L_2$ of focal lengths $0.20 \,m$ and $0.10 \,m$ respectively,as depicted in the figure. The separation between the lenses is $0.30 \,m$. The final image formed by this two-lens system is at

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