The radius of curvature of a lens is $20\,cm$ and its refractive index is $1.5$. If the refractive index of the surrounding liquid is $1.6$,then the focal length of the system is .......... $cm$.

$A$ plano-convex lens has a focal length of $20\,cm$. If its plane surface is silvered,it behaves as a converging mirror. What will be its focal length in $cm$?

$A$ concave mirror of focal length $f_{1}$ is placed at a distance $d$ from a convex lens of focal length $f_{2}$. $A$ parallel beam of light coming from infinity parallel to the principal axis falls on the convex lens and then after refraction falls on the concave mirror. If the light is to retrace its path,the distance $d$ should be:

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.......$cm$.

An object is placed at a distance of $12 \,{cm}$ from a convex lens. $A$ convex mirror of focal length $15 \,{cm}$ is placed on the other side of the lens at $8 \,{cm}$ as shown in the figure. The image of the object coincides with the object. When the convex mirror is removed,a real and inverted image is formed at a position. The distance of this image from the object will be ..... $(cm)$.

The distance between a convex lens and a plane mirror is $10 \, cm$. The parallel rays incident on the convex lens after reflection from the mirror form an image at the optical centre of the lens. The focal length of the lens will be.....$cm$.