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 similar thin equi-convex lenses,each of focal length $f$,are kept coaxially in contact with each other such that the focal length of the combination is $F_{1}$. When the space between the two lenses is filled with glycerin (which has the same refractive index $\mu = 1.5$ as that of glass),the equivalent focal length is $F_{2}$. The ratio $F_{1} : F_{2}$ will be

$A$ convex lens of focal length $30 \ cm$ is placed in contact with a concave lens of focal length $20 \ cm$. An object is placed at $20 \ cm$ to the left of this lens system. The distance of the image from the lens in $cm$ is . . . . . .

$A$ lens of power $+2 \text{ D}$ is placed in contact with a lens of power $-1 \text{ D}$. The combination will behave like:

$A$ real image of an object is formed at a distance of $20 \, cm$ from a lens. On putting another identical lens in contact with it,the image is shifted $10 \, cm$ towards the combination. The power of the lens is (in $, D$)

$A$ parallel beam of light is incident on a system of two convex lenses with focal lengths $f_1 = 20 \, cm$ and $f_2 = 10 \, cm$. What should be the distance between the two lenses so that the rays,after refraction from both lenses,emerge as a parallel beam? (in $cm$)