To determine the refractive index of a glass slab using a travelling microscope, the minimum number of readings required is:

$A$ 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 . . . $cm$.

$A$ light ray enters a rectangular glass slab of refractive index $\sqrt{3}$ at an angle of incidence of $60^{\circ}$. It travels a distance of $5 \, cm$ inside the slab and emerges out. What is the perpendicular distance between the incident and emergent ray?

$A$ ray of light is incident from air on a glass plate having thickness $\sqrt{3} \, cm$ and refractive index $\sqrt{2}$. The angle of incidence of the ray is equal to the critical angle for the glass-air interface. The lateral displacement of the ray when it passes through the plate is $....... \times 10^{-2} \, cm$ (given $\sin 15^{\circ} = 0.26$).

$A$ glass tumbler having an inner depth of $17.5 \, cm$ is kept on a table. $A$ student starts pouring water $(\mu = 4/3)$ into it while looking at the surface of water from above. When he feels that the tumbler is half-filled,he stops pouring water. Up to what height,the tumbler is actually filled? (In $cm$)

$A$ container contains a liquid with refractive index of $1.2$ up to a height of $60 \ cm$ and another liquid having refractive index $1.6$ is added to height $H$ above the first liquid. If viewed from above,the apparent shift in the position of the bottom of the container is $40 \ cm$. The value of $H$ is . . . . . . $\ cm$. (Consider liquids are immiscible)