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.....$cm$.

$A$ concave lens of focal length $20 \ cm$ placed in contact with a plane mirror acts as a

The focal length of a planoconvex glass lens is $20 \,cm$ $(\mu_g=1.5)$. The plane face of it is silvered. An illuminating object is placed at a distance of $60 \,cm$ from the lens on its axis along the convex side. Then the distance (in $cm$) of the image is .........

Two identical symmetric double convex lenses of focal length $f$ are cut into two equal parts $L_1, L_2$ by the $AB$ plane and $L_3, L_4$ by the $XY$ plane as shown in the figure respectively. The ratio of the focal lengths of lenses $L_1$ and $L_3$ is

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 $\,cm$)

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