Up to what height should we fill a glass of $21\, cm$ height so that it may appear half-filled? (Assume the refractive index of the liquid is $\mu = 1.5$)

$A$ plane mirror is placed at the bottom of a tank containing a liquid of refractive index ' $\mu$ '. ' $P$ ' is a small object at a height ' $h$ ' above the mirror. An observer ' $O$ ' vertically above ' $P$ ' outside the liquid sees ' $P$ ' and its image in the mirror. The apparent distance between these two will be

$A$ bubble in a glass slab (refractive index $1.5$) when viewed from one side appears at $5 \,cm$ and at $2 \,cm$ from the other side. Then the thickness of the slab is: (in $\,cm$)

What is the time taken (in seconds) for light to cross a glass slab of thickness $4 \ mm$ and refractive index $\mu = 3$?

An ink mark is made on a piece of paper. $A$ glass slab of thickness $t$ is placed on it. The ink mark appears to be raised up through a distance $x$ when viewed at nearly normal incidence. If the refractive index of the material of the glass slab is $\mu$,then the thickness of the glass slab $t$ is given by:

Mention the relation between the real depth and the apparent depth in terms of the refractive indices of the media.