Given that, the velocity of light in quartz = $1.5\times {10}^{\mathrm{8 }}\mathrm{m} {\mathrm{s}}^{-1}$ and the velocity of light in glycerine = $\frac{9}{4}\times {10}^{\mathrm{8 }}\mathrm{m} {\mathrm{s}}^{-1}$. If a slab made of quartz is placed in front of an object kept in glycerine (as shown in the figure), then the shift of the object produced by slab is

  

A small coin is fixed at the center of the base of an empty cylindrical steel container having radius $R=1 \mathrm{m}$ and height $d=4 \mathrm{m}$. At time $t=0 \mathrm{s}$, the container starts getting filled with water at a flowrate of $Q=0.1 {\mathrm{m}}^3/\mathrm{s}$ without disturbing the coin. Find the approximate time when the coin will first be seen by the observer "$O$" from the height of $H=5.75 \mathrm{m}$ above and $L=1.5 \mathrm{m}$ radially away from the coin as shown in the figure. Refractive index of water is $n=1.33$.

A diver swims obliquely above a fish in water. If he wants to hit the fish, he must aim