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

$A$ paraxial beam is incident on a glass $(n = 1.5)$ hemisphere of radius $R = 6\, cm$ in air as shown. The distance of the point of convergence $F$ from the plane surface of the hemisphere is......$cm$.

$A$ beam of light is converging towards a point $I$ on a screen. $A$ plane glass plate of thickness $t$ and refractive index $\mu$ is introduced in the path of the beam. The convergence point is shifted by:

$A$ 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?

$A$ composite slab consisting of different media is placed in front of a concave mirror of radius of curvature $150 \, cm$. The whole arrangement is placed in water (refractive index $\mu = 4/3$). An object $O$ is placed at a distance $20 \, cm$ from the slab. The refractive indices of the different media are given in the diagram. Find the final image formed by the system.

How much water should be filled in a container $21 \ cm$ in height,so that it appears half-filled when viewed from the top of the container? (Given that refractive index of water $\mu = 4/3$)