$A$ convergent doublet of separated lenses,corrected for spherical aberration,has a resultant focal length of $10\,cm$. The separation between the two lenses is $2\,cm$. The focal lengths of the component lenses are:

Two lenses of power $+12 \ D$ and $-2 \ D$ are placed in contact. What will be the focal length of the combination in $cm$?

Two convex lenses ($L_1$ and $L_2$) of equal focal length $f$ are placed at a distance $\frac{f}{2}$ apart. An object is placed at a distance $4f$ to the left of $L_1$ as shown in the figure. The final image is at:

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

$A$ 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 are of the same radius of curvature $R = 14 \, cm$. For this bi-convex lens,for an object distance of $40 \, cm$,the image distance will be.......$cm$

An object is located $4 \ m$ from the first of two thin converging lenses of focal lengths $2 \ m$ and $1 \ m,$ respectively. The lenses are separated by $3 \ m$. The final image formed by the second lens is located from the source at a distance of (in $m$):