Some water is filled in a container of height $30 \, cm$. If it is to appear half-filled to the observer when viewed from the top of the container, the height up to which water should be filled in it is [Refractive index of water $= \frac{4}{3}$] (in $cm$)

Two transparent slabs have the same thickness as shown. One is made of material $A$ of refractive index $1.5$. The other is made of two materials $B$ and $C$ with thickness in the ratio $1 : 2$. The refractive index of $C$ is $1.6$. If a monochromatic parallel beam passing through the slabs has the same number of waves inside both,the refractive index of $B$ is

$A$ bubble in a glass slab $(\mu = 1.5)$ when viewed from one side appears at $5 \ cm$ and from the other side appears at $2 \ cm$. The thickness of the slab is .... $cm$.

$A$ large glass slab $\left( \mu = \frac{5}{3} \right)$ of thickness $8 \, cm$ is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius $R \, cm$. What is the value of $R$? ....... $cm$

$A$ microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\mu = \frac{5}{3}$ is poured inside the bucket,then the microscope has to be raised by $30\,cm$ to focus the object again. The height of the liquid in the bucket is $..........\,cm$.

$A$ vessel of depth $x$ is half filled with oil of refractive index $\mu_1$ and the other half is filled with water of refractive index $\mu_2$. The apparent depth of the vessel when viewed from above is