$A$ ray of light is incident at an angle of incidence $60^{\circ}$ on a glass slab of refractive index $\sqrt{3}$. After refraction,the light ray emerges out from the other parallel face,and the lateral shift between the incident ray and the emergent ray is $4 \sqrt{3} \, cm$. The thickness of the glass slab is . . . $cm$.

What is the time taken (in seconds) for light to cross a glass slab of thickness $4 \ mm$ and refractive index $\mu = 3$?

In a vessel of $21 \, cm$ depth,up to what height should water be filled so that it appears to be $20\%$ filled when viewed from the top (in $, cm$)? (Given: $\mu_{water} = 4/3$)

$A$ concave mirror is placed over a beaker containing water of refractive index $\mu = 1.33$. The object is placed at the bottom of the beaker. If the image of the object is formed at a distance of $25 \, cm$ from the top surface of the water,and the mirror is at a height of $15 \, cm$ above the water surface,find the focal length of the mirror in $cm$.

$AB$ 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

$A$ man standing in a swimming pool looks at a stone lying at the bottom. The depth of the swimming pool is $h$. At what distance from the surface of water is the image of the stone formed? (Line of vision is normal; Refractive index of water is $n$)