Two thin lenses of focal lengths $f_1$ and $f_2$ are in contact and coaxial. The combination is equivalent to a single lens of power:

$A$ bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. The refractive index $n$ of the first lens is $1.5$ and that of the second lens is $1.2$. Both the curved surfaces have the same radius of curvature $R = 14 \ cm$. For this bi-convex lens,if the object distance is $40 \ cm$,what will be the image distance (in $cm$)?

$A$ thin convex lens of focal length $5 \ cm$ and a thin concave lens of focal length $4 \ cm$ are combined together (without any gap) and this combination has magnification $m_1$, when an object is placed $10 \ cm$ before the convex lens. Keeping the positions of the convex lens and object undisturbed, a gap of $1 \ cm$ is introduced between the lenses by moving the concave lens away, which leads to a change in the magnification of the total lens system to $m_2$. The value of $\left|\frac{m_1}{m_2}\right|$ is . . . . . . .

The plane faces of two identical plano-convex lenses,each having a focal length of $40 \ cm$,are pressed against each other to form a biconvex lens. The distance from this lens at which an object must be placed to obtain a real,inverted image with a magnification of $1$ is ....... $cm$.

Two lenses have focal lengths of $+10 \ cm$ and $-15 \ cm$. When they are placed in contact,the combination acts as a convex lens. If the chromatic aberration is zero,what is the ratio of their dispersive powers?

In which optical instruments is a combination of lenses used?