$A$ 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 $; cm$)?

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.......$cm$.

$A$ 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 $...\,cm$.

$A$ 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:

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 equiconvex lens of focal length $F$ is cut into two equal parts along the vertical axis. The focal length of each part will be