$A$ symmetric double convex lens is cut into two equal parts by a plane perpendicular to the principal axis. If the power of the original lens was $4 \ D$,what will be the power of each cut lens (in $D$)?

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.....$cm$.

An equiconvex lens of radius of curvature $R = 20 \, cm$ and refractive index $\mu = 1.5$ is silvered on one side. The equivalent focal length of the system is: (in $, cm$)

$A$ plano-convex lens $(\mu = 1.5)$ has a radius of curvature of $10 \; cm$. It is silvered on its plane surface. Find the focal length after silvering. (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 $...\,cm$.

One face of a rectangular glass plate $6 \, cm$ thick is silvered. An object held $8 \, cm$ in front of the first face forms an image $12 \, cm$ behind the silvered face. The refractive index of the glass is