$A$ combination of two thin convex lenses of focal lengths $0.3 \, m$ and $0.1 \, m$ will have minimum spherical and chromatic aberrations if the distance between them is . . . . . . $m$.

Find the equivalent focal length of a combination of two convex lenses in contact,each having a focal length of $30 \ cm$. (in $cm$)

Two plano-convex lenses,each of focal length $10 \, cm$ and refractive index $3/2$,are placed as shown in the figure. The space between them is filled with water $\left( \mu = 4/3 \right)$. The whole arrangement is in air. The optical power of the system is ....... $D$.

Find the position of the final image formed by the combination of the three lenses shown in the figure. The focal lengths are $f_1 = 10 \ cm$,$f_2 = -10 \ cm$,and $f_3 = 30 \ cm$.

Concave and convex lenses are placed touching each other. The ratio of the magnitudes of their power is $2:3$. The focal length of the system is $30 \ cm$. Then the focal lengths of the individual lenses are:

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.)