An equiconvex lens of radius of curvature $R = 20 \, cm$ and refractive index $\mu = 1.5$ is silvered on one side. The equivalent focal length of the system is: (in $, cm$)

An object is placed in front of a thin convex lens of focal length $30\, cm$ and a plane mirror is placed $15\, cm$ behind the lens. If the final image of the object coincides with the object,the distance of the object from the lens is.....$cm$.

An equiconvex lens of glass of focal length $0.1 \text{ m}$ is cut along a plane perpendicular to the principal axis into two equal parts. The ratio of the focal lengths of the new lenses formed is

Two thin similar convex lenses are joined together front to front with the rear portion silvered such that a sharp image of an object at infinity is formed $20 \, cm$ from the mirror. When the air between the lenses is replaced by water $(\mu_w = 4/3)$,then the image formed by the mirror is at a distance of ........ $cm$.

In the diagram given below,there are three lenses formed. Considering the negligible thickness of each of them as compared to $|R_1|$ and $|R_2|$,i.e.,the radii of curvature for the upper and lower surfaces of the glass lens,the power of the combination is:

Two identical symmetric double convex lenses of focal length $f$ are cut into two equal parts $L_1, L_2$ by the $AB$ plane and $L_3, L_4$ by the $XY$ plane as shown in the figure respectively. The ratio of the focal lengths of lenses $L_1$ and $L_3$ is