$A$ convex lens of focal length $30\, cm$ and a concave lens of focal length $10\, cm$ are placed coaxially at a distance $d$ apart. Parallel rays are incident on the convex lens. The rays emerging from the concave lens are also parallel. Then $d = $ . . . . . . $cm$.

$A$ parallel beam of light is incident on a system of two convex lenses of 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 the lenses emerge as a parallel beam (in $, cm$)? (Note: The condition for the final rays to emerge parallel is that the focal point of the first lens must coincide with the focal point of the second lens).

Find the position of the final image with respect to the rightmost lens formed by the lens combination shown in the figure.

$A$ lens of power $3.5 \, D$ is placed in contact with a lens of power $-2.5 \, D$. The combination behaves as:

An eye specialist prescribes spectacles having a combination of a convex lens of focal length $40\, cm$ in contact with a concave lens of focal length $25\, cm$. The power of this lens combination in diopters is

The focal length of a lens of dispersive power $0.45$ which should be placed in contact with a convex lens of focal length $84 \,cm$ and dispersive power $0.21$ to make the achromatic combination from the two lenses,in $cm$ is