$A$ thin plano-convex lens acts like a concave mirror of focal length $0.2 \ m$ when silvered from its plane surface. The refractive index of the material of the lens is $1.5$. The radius of curvature of the convex surface of the lens will be.......$m$.

Consider a concave mirror and a convex lens (refractive index $=1.5$) of focal length $10 \ cm$ each,separated by a distance of $50 \ cm$ in air (refractive index $=1$) as shown in the figure. An object is placed at a distance of $15 \ cm$ from the mirror. Its erect image formed by this combination has magnification $M_1$. When the setup is kept in a medium of refractive index $7/6$,the magnification becomes $M_2$. The magnitude $\left|\frac{M_2}{M_1}\right|$ is

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

An object is placed at a distance of $30\,cm$ from a convex lens of focal length $20\,cm$. At what distance (in $cm$) from the lens on the other side should a convex mirror of radius of curvature $10\,cm$ be placed so that the images formed by the lens and the mirror coincide?

An equiconvex lens of focal length $F$ is cut into two equal parts along the vertical axis. The focal length of each 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?