Two planoconvex lenses each of focal length $10 \, cm$ and refractive index $3/2$ are placed as shown. In the space left, water $(R.I = 4/3)$ is filled. The whole arrangement is in air. The optical power of the system is (in diopters):

$A$ 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 $D$)

$A$ collimated beam of light of diameter $2 \ mm$ is propagating along the $x$-axis. The beam is required to be expanded into a collimated beam of diameter $14 \ mm$ using a system of two convex lenses. If the first lens has a focal length of $40 \ mm$, then the focal length of the second lens is . . . . . . $mm$.

$A$ parallel beam of light is incident on a system of two convex lenses with focal lengths $f_1 = 20 \, cm$ and $f_2 = 10 \, cm$. What should be the distance between the two lenses so that the rays,after refraction from both lenses,emerge as a parallel beam? (in $cm$)

$A$ convex lens of focal length $f$ is cut along the dashed line as shown in the figure. What is the focal length of each part?

$A$ diverging lens with a focal length magnitude of $25\ cm$ is placed at a distance of $15\ cm$ from a converging lens with a focal length magnitude of $20\ cm$. $A$ beam of parallel light falls on the diverging lens. The final image formed is: