An optical device is constructed by fixing three identical convex lenses of focal lengths $10 \,cm$ each inside a hollow tube at equal spacing of $30 \,cm$ each. One end of the device is placed $10 \,cm$ away from a point source. What is the image shift in $cm$ when the device is moved away from the source by another $10 \,cm$?

$A$ combination of two thin lenses with focal lengths $f_1$ and $f_2$ respectively forms an image of a distant object at a distance of $60 \ cm$ when the lenses are in contact. The position of this image shifts by $30 \ cm$ towards the combination when the two lenses are separated by $10 \ cm$. The corresponding values of $f_1$ and $f_2$ are:

The two lenses of an achromatic doublet should have:

$A$ convex lens of focal length $10 \, cm$ is placed in contact with a concave lens. The focal length of the combination is numerically equal to that of the concave lens. The focal length of the concave lens is ............ $cm$.

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:

$A$ convex lens of focal length $30 \ cm$ forms an image of height $2 \ cm$ for an object situated at infinity. If a concave lens of focal length $20 \ cm$ is placed coaxially at a distance of $26 \ cm$ in front of the convex lens,what will be the size of the final image in $cm$?