$A$ large glass slab $\left( \mu = \frac{5}{3} \right)$ of thickness $8 \, cm$ is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius $R \, cm$. What is the value of $R$? ....... $cm$

$A$ bird is flying $3\, m$ above the surface of water. If the bird is diving vertically down with speed $= 6\, m/s$,its apparent velocity as seen by a stationary fish underwater is $m/s$.

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 $4/3$).

$A$ beam of light is converging towards a point $I$ on a screen. $A$ plane glass plate of thickness $t$ and refractive index $\mu$ is introduced in the path of the beam. The convergence point is shifted by:

$A$ container is half-filled with a liquid of refractive index $\mu$. The other half is filled with an immiscible liquid of refractive index $1.5\mu$. If the apparent depth of the container is $1.5$ times the actual depth, find $\mu$.

$A$ transparent cube of $15\, cm$ edge contains a small air bubble. Its apparent depth when viewed through one face is $6\, cm$ and when viewed through the opposite face is $4\, cm$. Then the refractive index of the material of the cube is