An underwater swimmer is at a depth of $12 \, m$ below the surface of water. $A$ bird is at a height of $18 \, m$ from the surface of water,directly above his eyes. For the swimmer,the bird appears to be at a distance from the surface of water equal to ....... $m$ (Refractive index of water is $4/3$).

$A$ fish rising vertically upward with a uniform velocity of $8\,ms^{-1}$ observes that a bird is diving vertically downward towards the fish with a velocity of $12\,ms^{-1}$. If the refractive index of water is $\frac{4}{3}$,then the actual velocity of the diving bird to pick the fish will be $.......\,ms^{-1}$.

$A$ 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.

$A$ printed page is pressed by a glass of water. The refractive index of the glass and water is $1.5$ and $1.33$,respectively. If the thickness of the bottom of the glass is $1\, cm$ and the depth of the water is $5\, cm$,how much will the page appear to be shifted if viewed from the top (in $,cm$)?

Light travels through a glass plate of thickness $t$ and having refractive index $\mu$. If $c$ is the velocity of light in vacuum,the time taken by the light to travel through this thickness of glass is:

$AB$ is an object of length $l$ dipped in water at a depth of $d$. It is viewed from air at near-normal incidence. The length of the image is