Three immiscible transparent liquids with refractive indices $3/2, 4/3$ and $6/5$ are arranged one above the other in a container. The depths of the liquids are $3 \text{ cm}, 4 \text{ cm}$ and $6 \text{ cm}$ respectively. The apparent depth of the vessel is (in $\text{ cm}$)

$A$ small pin fixed on a table top is viewed from above from a distance of $50 \, cm$. By what distance would the pin appear to be raised if it is viewed from the same point through a $15 \, cm$ thick glass slab held parallel to the table? Refractive index of glass $= 1.5$. Does the answer depend on the location of the slab?

$A$ vessel is filled with two different liquids which do not mix. One liquid is $40 \ cm$ deep with a refractive index of $1.6$,and the other is $30 \ cm$ deep with a refractive index of $1.5$. What is the apparent depth of the vessel when viewed normally (in $cm$)?

$A$ fish at a depth of $12 \, cm$ in water is viewed by an observer on the bank of a lake. To what height is the image of the fish raised? (Refractive index of water $\mu = 4/3$)

$A$ 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

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