An equiconvex lens has power $P$. It is cut into two symmetrical halves by a plane containing the principal axis. The power of one part will be

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.......$cm$.

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.....$cm$.

The diagram shows a silvered equiconvex lens. An object of length $1\,cm$ is placed at a distance of $30\,cm$ in front of the lens. What will be the final image properties? The refractive index of the lens is $\mu$ and the refractive index of the medium in which the lens has been placed is $2\mu$. Both surfaces have a radius of curvature $R$.

$A$ biconvex lens of focal length $15 \,cm$ is in front of a plane mirror. The distance between the lens and the mirror is $10 \,cm$. $A$ small object is kept at a distance of $30 \,cm$ from the lens. The final image is

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: