$A$ microscope is focussed on a coin lying at the bottom of a beaker. The microscope is now raised up by $1 \, cm$. To what depth should the water be poured into the beaker so that the coin is again in focus? (Refractive index of water is $\frac{4}{3}$)

$A$ 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:

$A$ container is filled with a liquid of refractive index $\mu_1$ up to a depth $d$ and another liquid of refractive index $\mu_2$ up to a depth $d$ is poured on top of it. What is the apparent depth of the container when viewed from above?

$A$ travelling microscope is focused on an ink dot marked on a glass slab $(\mu = 1.5)$ of thickness $0.12 \,m$. By what distance should the microscope be moved to focus on the ink dot again after the slab is placed?

$A$ monochromatic light wave is incident normally on a glass slab of thickness $d$,as shown in the figure. The refractive index of the slab increases linearly from $n_1$ to $n_2$ over the height $h$. Which of the following statement$(s)$ is (are) true about the light wave emerging out of the slab?

$A$ 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)