$A$ 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 $\frac{4}{3}$)

$A$ 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 $..........\,cm$.

Two transparent slabs have the same thickness $t$. One is made of material $X$ of refractive index $1.5$. The other is made of two materials $Y$ and $Z$ having thicknesses in the ratio $1 : 2$. The refractive index of $Z$ is $1.6$. If a monochromatic parallel beam passing through the slabs has the same number of wavelengths inside both,the refractive index of $Y$ is

$A$ ray of light is incident on a parallel slab of thickness $t$ and refractive index $n$. If the angle of incidence $\theta$ is small,then the lateral displacement between the incident and emergent ray will be:

$A$ 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:

$A$ glass slab of thickness $4 \ cm$ contains the same number of waves as $5 \ cm$ of water when both are traversed by the same monochromatic ray of light. The refractive index of water is $4/3$. What is the refractive index of glass?