An object is placed at a distance of $15\;cm$ from a convex lens of focal length $10\;cm$. On the other side of the lens,a convex mirror is placed such that the image formed by the combination coincides with the object itself. Find the focal length of the convex mirror if the distance between the lens and the mirror is $30\;cm$. (in $;cm$)

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 $\,cm$)

The flat face of a plano-convex lens of focal length $10 \,cm$ is silvered. $A$ point source placed $30 \,cm$ in front of the curved surface will produce a

In an experiment,a convex lens of focal length $15 \, cm$ is placed coaxially on an optical bench in front of a convex mirror at a distance of $5 \, cm$ from it. It is found that an object and its image coincide if the object is placed at a distance of $20 \, cm$ from the lens. The focal length of the convex mirror is.......$cm$.

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

The two surfaces of a biconvex lens have the same radii of curvature. This lens is made of glass of refractive index $1.5$ and has a focal length $10 \ cm$ in air. The lens is cut into two equal halves along a plane perpendicular to its principal axis to yield two plano-convex lenses. The two pieces are glued such that the convex surfaces touch each other. If this combination lens is immersed in water (refractive index $= 4/3$), its focal length (in $cm$) is: