$A$ 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 $cm$?

$A$ lens of power $+2$ diopters is placed in contact with a lens of power $-1$ diopter. The combination will behave like

$A$ combination of two thin lenses of the same material with focal lengths $f_1$ and $f_2$,arranged on a common axis,minimizes chromatic aberration if the distance between them is:

One plano-convex and one plano-concave lens of same radius of curvature $R$ but of different materials are joined side by side as shown in the figure. If the refractive index of the material of $1$ is $\mu_1$ and that of $2$ is $\mu_2$,then the focal length of the combination is

The lens combination consists of two lenses, $L_1$ and $L_2$, of focal lengths $+10 \text{ cm}$ and $-10 \text{ cm}$, respectively. The object is placed at a distance of $30 \text{ cm}$ from the first lens $L_1$. The distance between the two lenses is $3 \text{ cm}$. Find the position of the final image formed.

$A$ 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: