$A$ plano-convex lens of focal length $30\,cm$ has its plane surface silvered. An object is placed $40\,cm$ from the lens on the convex side. The distance of the image from the lens is.......$cm$

$A$ convex lens of focal length $20 \, cm$ and a concave mirror of focal length $f$ are placed coaxially at a distance of $5 \, cm$ apart. $A$ parallel beam of light incident on the convex lens emerges from the system as a parallel beam. Then $f = \dots \, cm$.

$A$ point-like object is placed at a distance of $1\, m$ in front of a convex lens of focal length $0.5\, m$. $A$ plane mirror is placed at a distance of $2\, m$ behind the lens. Find the position and nature of the final image formed by the system.

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?

$A$ point object is placed at a distance of $20 \, cm$ from a thin plano-convex lens of focal length $15 \, cm$. If the plane surface is silvered,where will the image form?

$A$ convex lens of focal length $15\,cm$ is placed in front of a convex mirror. When an object is placed at $O$,the image coincides with it. The radius of curvature of the mirror is.....$cm$.