$A$ travelling microscope is focused on an ink dot marked on a glass slab $(\mu = 1.5)$ of thickness $0.12 \,m$. By what distance should the microscope be moved to focus on the ink dot again after the slab is placed?

$A$ 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 $= 1.5$)

An air bubble in a glass slab with refractive index $1.5$ (near normal incidence) is $5\, cm$ deep when viewed from one surface and $3\, cm$ deep when viewed from the opposite face. The thickness (in $cm$) of the slab is

$A$ convex lens with lateral magnification $2$ is used to image a point at the bottom of a tank. The image of the point is formed $60 \ cm$ above the lens. Now a liquid is filled into the tank to a height of $24 \ cm$. It is found that the distance of the image of the same point is now $120 \ cm$ above the lens. Find the refractive index of the liquid.

$A$ vessel of depth $d$ is half filled with oil of refractive index $n_1$ and the other half is filled with water of refractive index $n_2$. The apparent depth of this vessel when viewed from above will be

$A$ beaker contains water up to a height $h_{1}$ and kerosene of height $h_{2}$ above water. The total height of (water $+$ kerosene) is $(h_{1} + h_{2})$. The refractive index of water is $\mu_{1}$ and that of kerosene is $\mu_{2}$. The apparent shift in the position of the bottom of the beaker when viewed from above is: