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 $D$)

An optician makes spectacles having a combination of a convex lens of focal length $40 \ cm$ in contact with a concave lens of focal length $25 \ cm$. The power of this combination of lenses in dioptre is:

Two thin lenses of focal lengths $20 \ cm$ and $25 \ cm$ are placed in contact. The effective power of the combination is (in $D$)

$A$ plano-convex lens (focal length $f_2,$ refractive index $\mu_2,$ radius of curvature $R$) fits exactly into a plano-concave lens (focal length $f_1,$ refractive index $\mu_1,$ radius of curvature $R$). Their plane surfaces are parallel to each other. Then,the focal length of the combination will be

$A$ glass convex lens of focal length $0.1 \ m$ is cut into two equal parts along its axis. The ratio of the focal length of the new lenses is:

$A$ thin convex lens of focal length $30 \, cm$ forms an image $2 \, cm$ high,of an object at infinity. $A$ thin concave lens of focal length $20 \, cm$ is placed $26 \, cm$ from the convex lens on the side of the image. The height of the final image is.....$cm$.