$A$ ray of light is incident normally on a glass slab of thickness $5 \ cm$ and refractive index $1.6$. The time taken by a ray to travel from the source of light to the surface of the slab is the same as the time taken to travel through the glass slab. The distance of the source from the surface is: (in $cm$)

$A$ 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 $= 1.5$)

$A$ 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.

$A$ 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 $\mu = 4/3$)

$A$ 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?

If the velocity of light in vacuum is $3 \times 10^{8} \text{ m/s}$, the time taken (in nanoseconds) to travel through a glass plate of thickness $10 \text{ cm}$ and refractive index $1.5$ is: