$A$ 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:

$A$ convergent lens is placed $40 \,cm$ to the right of a diverging lens of focal length $15 \,cm$. $A$ parallel beam of light enters the diverging lens from the left, and the beam is again parallel when it emerges from the convergent lens. The focal length of the convergent lens is (in $\,cm$)

Two thin lenses of focal lengths $f_1$ and $f_2$ are in contact and coaxial. The power of the combination is

Find the equivalent focal length of a combination of two convex lenses in contact,each having a focal length of $30 \ cm$. (in $cm$)

An achromatic convergent lens of focal length $20 \, cm$ is made of two lenses (in contact) of materials having dispersive powers in the ratio of $1 : 2$ and having focal lengths $f_1$ and $f_2$. Which of the following is true?

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