An object is placed in front of a thin convex lens of focal length $30\, cm$ and a plane mirror is placed $15\, cm$ behind the lens. If the final image of the object coincides with the object,the distance of the object from the lens is.....$cm$.

$A$ plano-convex lens $(f = 20 \ cm)$ is silvered at the plane surface. Now,the new focal length $F$ will be........$cm$.

Two identical thin plano-convex glass lenses (refractive index $1.5$) each having a radius of curvature of $20\, cm$ are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index $1.7$. The focal length of the combination is.......$cm$.

The plane surface of a plano-convex lens of focal length $f$ is silvered. It will behave as

$A$ point source of light is placed at $2f$ from a converging lens of focal length $f$. $A$ flat mirror is placed on the other side of the lens at a distance $d$ such that rays reflected from the mirror are parallel after passing through the lens again. If $f=30 \, cm$,then $d$ is equal to ............. $cm$.

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?