As shown in the figure,a plane mirror is fixed at a height of $50\,cm$ from the bottom of a tank containing water $\left(\mu = \frac{4}{3}\right)$. The height of water in the tank is $8\,cm$. $A$ small bulb is placed at the bottom of the water tank. The distance of the image of the bulb formed by the mirror from the bottom of the tank is $......\,cm$.

$A$ light wave is incident normally on a glass slab of refractive index $1.5$. If $4\%$ of light gets reflected and the amplitude of the electric field of the incident light is $30\, V/m$,then the amplitude of the electric field for the wave propagating in the glass medium will be.......$ V/m$

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

Consider a configuration of $n$ identical units,each consisting of three layers. The first layer is a column of air of height $h=\frac{1}{3} \text{ cm}$,and the second and third layers are of equal thickness $d=\frac{\sqrt{3}-1}{2} \text{ cm}$,and refractive indices $\mu_1=\sqrt{\frac{3}{2}}$ and $\mu_2=\sqrt{3}$,respectively. $A$ light source $O$ is placed on the top of the first unit,as shown in the figure. $A$ ray of light from $O$ is incident on the second layer of the first unit at an angle of $\theta=60^{\circ}$ to the normal. For a specific value of $n$,the ray of light emerges from the bottom of the configuration at a distance $l=\frac{8}{\sqrt{3}} \text{ cm}$,as shown in the figure. The value of $n$ is. . . . .

Two immiscible liquids of refractive indices $\frac{8}{5}$ and $\frac{3}{2}$ respectively are put in a beaker as shown in the figure. The height of each column is $6 \,cm$. $A$ coin is placed at the bottom of the beaker. For near normal vision,the apparent depth of the coin is $\frac{\alpha}{4} \,cm$. The value of $\alpha$ is . . . . . . .

$A$ beaker contains water up to a height of $h_1$ and kerosene above the water up to a height of $h_2$. The total height is $(h_1 + h_2)$. The refractive index of water is $\mu_1$ and that of kerosene is $\mu_2$. What is the apparent shift of the bottom of the beaker when viewed from above?