$A$ 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 $cm$)?

The apparent depth of a needle lying at the bottom of a tank,which is filled with water of refractive index $1.33$ to a height of $12.5\,cm$,is measured by a microscope to be $9.4\,cm$. If water is replaced by a liquid of refractive index $1.5$ up to the same height,what distance would the microscope have to be moved to focus on the needle again (in $,cm$)?

$A$ ray of light travelling through a rarer medium is incident at a very small angle $i$ on a glass slab,and after refraction,its velocity is reduced by $20 \%$. The angle of deviation is:

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:

$A$ container is filled with a liquid of refractive index $\mu_1$ up to a depth $d$ and another liquid of refractive index $\mu_2$ up to a depth $d$ is poured on top of it. What is the apparent depth of the container when viewed from above?

$A$ 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?