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

$A$ plano-convex lens (focal length $f_2,$ refractive index $\mu_2,$ radius of curvature $R$) fits exactly into a plano-concave lens (focal length $f_1,$ refractive index $\mu_1,$ radius of curvature $R$). Their plane surfaces are parallel to each other. Then,the focal length of the combination will be

Three thin lenses are combined by placing them in contact with each other to get more magnification in an optical instrument. Each lens has a focal length of $3 \,cm$. If the least distance of distinct vision is taken as $25 \,cm$, the total magnification of the lens combination in normal adjustment is

Two lenses of power $3\,D$ and $-5\,D$ are combined to form a compound lens. An object is placed at a distance of $50\,cm$ from this combination. At what distance (in $cm$) will the image be formed?

Find the linear magnification in the given diagram.

The ratio of the dispersive powers of two lenses is $4:3$. If the achromatic combination of these two lenses in contact is a convex lens of focal length $60 \, cm$,find the focal lengths of the component lenses.