$A$ 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:

Two thin convex lenses of focal length $f_1$ and $f_2$ are placed in contact with each other. The equivalent power of the lens combination is . . . . . . .

Two thin convex lenses of focal lengths $30 \ cm$ and $10 \ cm$ are placed coaxially,$1 \ cm$ apart. The power of this combination is (in $D$)

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.

$A$ 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.......$cm$

What is the focal length of a convex lens of focal length $30 \ cm$ in contact with a concave lens of focal length $10 \ cm$? (Ignore the thickness of the lenses.)