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.

Given a thin convex lens (refractive index $\mu_2$),kept in a liquid (refractive index $\mu_1, \mu_1 < \mu_2$) having radii of curvature $|R_1|$ and $|R_2|$. Its second surface is silver-polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

$A$ 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 $...\,cm$.

An object is placed $0.1 \,m$ in front of a convex lens of focal length $20 \,cm$ made of a material of refractive index $1.5$. The surface of the lens away from the object is silvered. If the radius of curvature of the silvered surface is $22 \,cm$,then the distance of the final image from the silvered surface is (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

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?