Two thin lenses,one of focal length $+ 60 \ cm$ and the other of focal length $-20 \ cm$ are put in contact. The combined focal length is........$cm$.

Two lenses of power $-15 \, D$ and $5 \, D$ are placed in contact with each other. The focal length of this combination 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 $cm$.

$A$ plano-convex lens of refractive index $\mu_1$ fits exactly into a plano-concave lens of refractive index $\mu_2$. Their plane surfaces are parallel to each other. $R$ is the radius of curvature of the curved surface of the lenses. The focal length of the combination is:

$A$ convex lens of focal length $30 \ cm$ and a concave lens of $10 \ cm$ focal length are placed so as to have the same axis. If a parallel beam of light falling on the convex lens leaves the concave lens as a parallel beam,then the distance between the two lenses will be.......$cm$.

Curved surfaces of a plano-convex lens of refractive index $\mu_{1}$ and a plano-concave lens of refractive index $\mu_{2}$ have equal radius of curvature as shown in the figure. Find the ratio of the radius of curvature to the focal length of the combined lenses.