$A$ convex lens of focal length $0.5 \ m$ and a concave lens of focal length $1 \ m$ are combined. The power of the resulting lens will be: (in $D$)

$A$ convex lens and a concave lens, each with a focal length of $4 \,cm$, are separated by a distance of $6 \,cm$ along their axis. An object is placed $8 \,cm$ before the convex lens. The distance between the object and its final image is (in $\,cm$)

Two thin lenses whose powers are $+2 \ D$ and $-4 \ D$ respectively are combined. The power of the combination is:

Two thin biconvex lenses have focal lengths $f_{1}$ and $f_{2}$. $A$ third thin biconcave lens has a focal length of $f_{3}$. If the two biconvex lenses are in contact,the total power of the lenses is $P_{1}$. If the first convex lens is in contact with the third lens,the total power is $P_{2}$. If the second lens is in contact with the third lens,the total power is $P_{3}$,then:

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:

Two thin convex lenses of focal length $f_1$ and $f_2$ are placed in contact with each other. The equivalent power of the lens combination is . . . . . . .