$A$ lens is placed on a plane mirror. An object needle and its image coincide at $15 \, cm$. The focal length of the lens is......$cm$.

$A$ plano-convex lens made of material of refractive index $\mu$ with radius of curvature $R$ is silvered on the curved side. How far away from the lens-mirror must you place a point object,so that the image coincides with the object?

$A$ convex lens has a focal length $f$. It is cut into two parts along the dotted line as shown in the figure. The focal length of each part will be

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 symmetrical convex lens with refractive index $1.5$ and radius of curvature $40 \, cm$. The surface of the lens further away from the object is silvered. Under auto-collimation condition,the object distance is.......$cm$.

Given is a thin convex lens of glass (refractive index $\mu$) and each side having radius of curvature $R$. One side is polished for complete reflection. At what distance from the lens,an object be placed on the optic axis so that the image gets formed on the object itself?