The time taken by sunlight to cross a $5 \,mm$ thick glass plate $(\mu = 3/2)$ 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 $\sin 15^{\circ} = 0.25$)

$A$ flat glass slab of thickness $6\, cm$ and refractive index $1.5$ is placed in front of a plane mirror. An observer is standing behind the glass slab and looking at the mirror. The actual distance of the observer from the mirror is $50\, cm$. The distance of his image from himself,as seen by the observer is .......$cm$.

$A$ glass hemisphere of radius $0.04\, m$ and refractive index $1.6$ is placed centrally over a cross mark on a paper:
$(i)$ with the flat face in contact with the paper;
$(ii)$ with the curved face in contact with the paper.
In each case,the cross mark is viewed directly from above. The positions of the images will be:

$A$ glass slab of thickness $20\, cm$ and refractive index $1.5$ is placed in front of a plane mirror. An object is placed at a distance of $40\, cm$ from the mirror in air. The position of the final image with respect to the mirror will be at a distance of:

The time required for light to pass through a glass slab of $2 \ mm$ thickness is $({\mu _{glass}} = 1.5)$.