The following figure represents two biconvex lenses $L_1$ and $L_2$ having focal lengths $10 \,cm$ and $15 \,cm$ respectively. The distance between $L_1$ and $L_2$ is: (in $\,cm$)

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

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

Two thin lenses,when in contact,produce a combination of power $+10 \, D$. When they are $0.25 \, m$ apart,the power reduces to $+6 \, D$. The focal lengths of the lenses (in $m$) are

Find the equivalent focal length of a combination of two convex lenses in contact,each having a focal length of $30 \ cm$. (in $cm$)

$A$ biconvex lens is formed by using two thin planoconvex lenses, as shown in the figure. The refractive index and radius of curved surfaces are also mentioned in the figure. When an object is placed on the left side of the lens at a distance of $30 \ cm$ from the biconvex lens, the magnification of the image will be: