$A$ converging lens of focal length $30 \,cm$ is placed in contact with another converging lens of unknown focal length. Then,the possible value for the focal length of the combination is ......... $cm$.

$A$ beam of parallel rays is brought to a focus by a plano-convex lens. $A$ thin concave lens of the same focal length is joined to the first lens. The effect of this is:

$A$ 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 $cm$?

$A$ bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. The refractive index $n$ of the first lens is $1.5$ and that of the second lens is $1.2$. Both the curved surfaces have the same radius of curvature $R = 14 \ cm$. For this bi-convex lens,if the object distance is $40 \ cm$,what will be the image distance (in $cm$)?

The focal length (in $cm$) of a lens with dispersive power $0.45$ that should be placed in contact with a convex lens of focal length $84 \,cm$ and dispersive power $0.21$ to form an achromatic combination is:

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):