Three immiscible transparent liquids with uniform refractive indices $\frac{3}{2}, \frac{4}{3}$ and $\frac{6}{5}$ are arranged one on top of another. The depths of the liquids are $3 \ cm, 4 \ cm$ and $6 \ cm$ respectively. The apparent depth of the vessel is (in $cm$)

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

$A$ glass cube of length $21 \ cm$ has a small air bubble trapped inside. When viewed normally from one face,its apparent distance is $8 \ cm$. When viewed normally from the opposite face,its apparent distance is $6 \ cm$. The refractive index of the glass and the actual distance of the air bubble from the first surface respectively are:

$A$ glass slab of thickness $4 \ cm$ contains the same number of waves as $5 \ cm$ of water when both are traversed by the same monochromatic ray of light. The refractive index of water is $4/3$. What is the refractive index of glass?

$A$ microscope is focussed on a coin lying at the bottom of a beaker. The microscope is now raised up by $1 \, cm$. To what depth should the water be poured into the beaker so that the coin is again in focus? (Refractive index of water is $\frac{4}{3}$)

$A$ rectangular glass block is placed on a mark made on the surface of a table and is viewed from a vertical direction. If the refractive index of the glass is $\mu$ and its thickness is $d$,by what distance will the mark appear to be raised?