Where should an object be placed so that a real and inverted image of the same size is obtained by a convex lens?

$A$ $10\, mm$ long awl pin is placed vertically in front of a concave mirror. $A$ $5\, mm$ long image of the awl pin is formed at $30\, cm$ in front of the mirror. The focal length of this mirror is ......... $cm$.

Two lenses of power $+3.5 D$ and $-2.5 D$ are placed in contact. Find the power and focal length of the lens combination.

Define absolute refractive index. Absolute refractive indices of medium $A$ and medium $B$ are $n_{a}$ and $n_{b}$ respectively. What is the refractive index of medium $B$ with respect to medium $A$? How does the velocity of light vary with change in the optical density of the media?

Define the term principal focus for a convex mirror.

$A$ beam of light is incident through the holes on side $A$ and emerges out of the holes on the other face of the box as shown in the Figure. Which of the following could be inside the box?