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 $\mu = 4/3$)

$A$ slab of glass,of thickness $6\, cm$ and refractive index $1.5$,is placed in front of a concave mirror,the faces of the slab being perpendicular to the principal axis of the mirror. If the radius of curvature of the mirror is $40\, cm$ and the reflected image coincides with the object,then the distance of the object from the mirror is.....$cm$

$A$ 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:

$A$ plane mirror is placed at the bottom of a tank containing a liquid of refractive index ' $\mu$ '. ' $P$ ' is a small object at a height ' $h$ ' above the mirror. An observer ' $O$ ' vertically above ' $P$ ' outside the liquid sees ' $P$ ' and its image in the mirror. The apparent distance between these two will be

$A$ 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 . . . $cm$.

$A$ glass cube of length $21 \ cm$ has a small air bubble trapped inside. When viewed normally from one face,its apparent distance is $8 \ cm$. When viewed normally from the opposite face,its apparent distance is $6 \ cm$. The refractive index of the glass and the actual distance of the air bubble from the first surface respectively are: