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

$A$ glass slab of thickness $3 \, cm$ and refractive index $3/2$ is placed on an ink mark on a piece of paper. The mark is viewed from a distance of $5.0 \, cm$ above the top surface of the slab. At what distance (in $cm$) will the mark appear to be?

$A$ 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$

$A$ 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 . . . $cm$.

$A$ 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?

$A$ layer of oil $3\,cm$ thick is floating on a layer of coloured water $5\,cm$ thick. The refractive index of coloured water is $5/3$ and the apparent depth of the two liquids appears to be $36/7\,cm$. Find the refractive index of oil.