$A$ luminous object is placed at a distance of $30 \,cm$ from a convex lens of focal length $20 \,cm$. On the other side of the lens,at what distance from the lens should a convex mirror of radius of curvature $10 \,cm$ be placed in order to have an upright image of the object coincident with it (in $,cm$)?

Consider a glass slab which is silvered at one side and the other side is transparent. The refractive index of the glass slab is $1.5$. If a ray of light is incident at an angle of $45^{\circ}$ on the transparent side,then the deviation of the ray of light from its initial path,when it comes out of the slab,is (in $^{\circ}$)

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 $;cm$)

$A$ plano-convex lens of refractive index $1.5$ and radius of curvature $30 \; cm$ is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens should an object be placed in order to have a real image of the size of the object (in $; cm$)?

An object is placed at a distance of $30\,cm$ from a convex lens of focal length $20\,cm$. At what distance (in $cm$) from the lens on the other side should a convex mirror of radius of curvature $10\,cm$ be placed so that the images formed by the lens and the mirror coincide?

$A$ plano-convex lens,when silvered on the plane side,behaves like a concave mirror of focal length $30 \ cm$. However,when silvered on the convex side,it behaves like a concave mirror of focal length $10 \ cm$. The refractive index of its material is: