An object is placed $30 \ cm$ away from a convex lens of focal length $10 \ cm$ and a sharp image is formed on a screen. Now,a concave lens is placed in contact with the convex lens. The screen now has to be moved by $45 \ cm$ to get a sharp image again. The magnitude of the focal length of the concave lens is (in $cm$):

Two thin convex lenses of focal lengths $20 \; cm$ and $25 \; cm$ are placed in contact. The effective power of the combination is:

The dispersive powers of two lenses are $0.01$ and $0.02.$ If the focal length of one lens is $+10\, cm$,what should be the focal length of the second lens so that they form an achromatic combination?

Two lenses of power $6 \, D$ and $-2 \, D$ are placed in contact to form a single lens. The focal length of the combination is:

Two thin lenses have a combined power of $+9 D$. When they are separated by a distance of $20 \,cm$, their equivalent power becomes $+\frac{27}{5} D$. Their individual powers (in diopters) are respectively:

Two thin biconvex lenses have focal lengths $f_{1}$ and $f_{2}$. $A$ third thin biconcave lens has a focal length of $f_{3}$. If the two biconvex lenses are in contact,the total power of the lenses is $P_{1}$. If the first convex lens is in contact with the third lens,the total power is $P_{2}$. If the second lens is in contact with the third lens,the total power is $P_{3}$,then: