$A$ plano-convex lens of refractive index $1.5$ and radius of curvature $30 \; cm$ is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens should an object be placed in order to have a real image of the size of the object (in $; cm$)?

An equiconvex lens has power $P$. It is cut into two symmetrical halves by a plane containing the principal axis. The power of one part will be

One face of a rectangular glass plate $6 \, cm$ thick is silvered. An object held $8 \, cm$ in front of the first face forms an image $12 \, cm$ behind the silvered face. The refractive index of the glass is

$A$ convex lens of focal length $20\,cm$ is placed in front of a convex mirror with their principal axes coinciding. The distance between the lens and the mirror is $10\,cm$. $A$ point object is placed on the principal axis at a distance of $60\,cm$ from the convex lens. The image formed by the combination coincides with the object itself. The focal length of the convex mirror 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?

The radius of the curved surface of a plano-convex lens is $20 \, cm$ and the refractive index of the lens material is $1.5$. Calculate the equivalent focal length of the lens if the curved surface is silvered.