An air bubble in a glass slab $(\mu = 1.5)$ is $5 \, cm$ deep when viewed from one face and $2 \, cm$ deep when viewed from the opposite face. The thickness of the slab is......$cm$

In the given diagram,the apparent velocity of a bird (coming toward a fish) as seen by the fish is $19 \, cm/s$. Find the actual velocity of the bird in $cm/s$.

$A$ bird is looking at a fish underwater from the air. $h_1$ is the height of the bird above the water surface and $h_2$ is the depth of the fish below the water surface. If $\mu$ is the refractive index of water with respect to air,then the distance of the fish as observed by the bird is:

$A$ light ray is incident on a glass slab of thickness $4 \sqrt{3} \text{ cm}$ and refractive index $\sqrt{2}$. The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of the ray after passing through the glass slab is . . . . . . $\text{cm}$. (Given $\sin 15^{\circ} = 0.25$)

$A$ vessel of depth $2d \ cm$ is half filled with a liquid of refractive index $\mu_1$ and the upper half with a liquid of refractive index $\mu_2$. The apparent depth of the vessel seen perpendicularly is

If the velocity of light in vacuum is $3 \times 10^{8} \text{ m/s}$, the time taken (in nanoseconds) to travel through a glass plate of thickness $10 \text{ cm}$ and refractive index $1.5$ is: