$A$ fish at a depth of $12 \, cm$ in water is viewed by an observer on the bank of a lake. To what height the image of the fish is raised? $....... \, cm$ (Refractive index of lake water $= 4/3$)

Two light rays initially in the same phase travel through two media of equal length $L$ having refractive indices $\mu_1$ and $\mu_2$ (where $\mu_1 > \mu_2$) as shown in the figure. If the wavelength of the light rays in air is $\lambda$,the phase difference of the emerging rays is given by:

$A$ glass slab is placed over letters of different colors. Which color letter will appear to be raised the least?

$A$ 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 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 $cm$)

$A$ vessel of depth $2h$ is half-filled with a liquid of refractive index $2\sqrt{2}$ and the upper half with another liquid of refractive index $\sqrt{2}$. The liquids are immiscible. The apparent depth of the inner surface of the bottom of the vessel will be:

$A$ fish and a bird are moving as shown in the figure. Find the velocity of the bird as observed by the fish.