$A$ convex lens of focal length $25 \ cm$ and a concave lens of focal length $10 \ cm$ are joined together. The power of the combination will be

$A$ combination of two thin convex lenses of focal lengths $0.3 \, m$ and $0.1 \, m$ will have minimum spherical and chromatic aberrations if the distance between them is . . . . . . $m$.

Two thin convex lenses of focal lengths $20 \; cm$ and $25 \; cm$ are placed in contact. The effective power of the combination is:

The dispersive powers of the materials of two lenses forming an achromatic combination are in the ratio of $4:3$. If the effective focal length of the combination is $+60 \ cm$,then the focal lengths of the lenses should be:

$A$ convex lens of focal length $20 \, cm$ is cut into two equal parts. This results in two plano-convex lenses as shown in the figure. These two parts are then placed in contact with each other as shown in the figure. What will be the focal length of the system in $cm$?

Two lenses of power $+5 \, D$ are placed at a distance $d$ to form sun goggles. The distance $d$ is . . . . . $cm$.