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.)

$A$ plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. The lenses are made of different materials with refractive indices $n_1$ and $n_2$,and $R$ is the radius of curvature of the curved surfaces. What is the focal length of the combination?

What is the position and nature of the image formed by the lens combination shown in the figure? ($f_1, f_2$ are focal lengths)

$A$ combination of two thin lenses in contact has a power of $+10 D$. The power reduces to $+6 D$ when the lenses are $0.25 m$ apart. The power of each individual lens is:

The focal length of a combination of lenses formed with lenses having powers of $+2.50 \ D$ and $-3.75 \ D$ will be .... $cm$.

Three lenses $L_1, L_2, L_3$ are placed co-axially as shown in the figure. The focal lengths of the lenses are $30 \, cm, 10 \, cm$ and $5 \, cm$ respectively. If a parallel beam of light falls on lens $L_1$ and emerges from $L_3$ as a convergent beam such that it converges at the focus of $L_3$,find the distance $d$ between $L_1$ and $L_2$ in $cm$.