Two lenses of power $+5 \, D$ are placed at a distance $d$ to form sun goggles. The distance $d$ is . . . . . $cm$.

Find the position of the final image formed by the combination of the three lenses shown in the figure. The focal lengths are $f_1 = 10 \ cm$,$f_2 = -10 \ cm$,and $f_3 = 30 \ cm$.

$A$ beam of parallel rays is brought to a focus by a plano-convex lens. $A$ thin concave lens of the same focal length is joined to the first lens. The effect of this 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?

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

Concave and convex lenses are placed touching each other. The ratio of the magnitudes of their power is $2:3$. The focal length of the system is $30 \ cm$. Then the focal lengths of the individual lenses are: